Frontiers in Complex Dynamics : : In Celebration of John Milnor's 80th Birthday (PMS-51) / / Araceli Bonifant, Scott Sutherland, Misha Lyubich.
John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightiet...
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Year of Publication: | 2014 |
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Bonifant, Araceli, author. aut http://id.loc.gov/vocabulary/relators/aut Frontiers in Complex Dynamics : In Celebration of John Milnor's 80th Birthday (PMS-51) / Araceli Bonifant, Scott Sutherland, Misha Lyubich. Course Book Princeton, NJ : Princeton University Press, [2014] ©2014 1 online resource (800 p.) : 32 color illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Mathematical Series Frontmatter -- Contents -- Preface -- Introduction -- Part I. One Complex Variable -- Arithmetic of Unicritical Polynomial Maps -- Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques -- Dynamical cores of topological polynomials -- The quadratic dynatomic curves are smooth and irreducible -- Multicorns are not path connected -- Leading monomials of escape regions -- Limiting behavior of Julia sets of singularly perturbed rational maps -- On (non-)local connectivity of some Julia sets -- Perturbations of weakly expanding critical orbits -- Unmating of rational maps: Sufficient criteria and examples -- A framework toward understanding the characterization of holomorphic dynamics -- Part II. One Real Variable -- Metric stability for random walks (with applications in renormalization theory) -- Milnor's conjecture on monotonicity of topological entropy: Results and questions -- Entropy in dimension one -- Part III. Several Complex Variables -- On Écalle-Hakim's theorems in holomorphic dynamics -- Index theorems for meromorphic self-maps of the projective space -- Dynamics of automorphisms of compact complex surfaces -- Bifurcation currents and equidistribution in parameter space -- Part IV. Laminations and Foliations -- Entropy for hyperbolic Riemann surface laminations I -- Entropy for hyperbolic Riemann surface laminations II -- Intersection theory for ergodic solenoids -- Invariants of four-manifolds with flows via cohomological field theory -- Color Plates -- Part V. Geometry and Algebra -- Two papers which changed my life: Milnor's seminal work on at manifolds and bundles -- Milnor's problem on the growth of groups and its consequences -- Contributors -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Differentiable dynamical systems. Dynamics. Functions of complex variables. MATHEMATICS / Combinatorics. bisacsh John Milnor. Jordan curves. Julia sets. K-theory. M. Hakim. Maldelbrot set. Milnor's conjecture. Sierpinski carpets. Sierpinski gaskets. Thurston Rigidity Theorem. William Thurston. antiholomorphic quadratic polynomials. antiholomorphic unicritical polynomials. arithmetics. asymptotic behavior. automorphisms. biholomorphisms. combinatorial group theory. complex manifolds. complex polynomials. conformal distortion. conjugacy. connectedness loci. critical objects. critical point. critically finite case. decomposition. differential geometry. differential topology. dynamical cores. dynamical derivatives. dynamical scales. dynamical systems. dynamics. eigenvalues. entropy theory. entropy. escape regions. expanding critical orbits. external rays. geometrically finite rational maps. global meromorphic maps. holomorphic dynamics studies. holomorphic dynamics. holomorphic germs. holomorphic maps. hyperbolic distortion. hyperbolic geometry. hyperbolicity. identity germ. implosions. index theorems. infinitely renormalizable quadratic polynomials. integral closure. interval dynamics. irreducibility. kneading sequences. laminations. leading monomial vector. leading monomials. limiting behavior. local connectivity. local dynamics. mathematics. mating. metric stability. monotonicity. multicorn. non-locally connected Julia sets. one-dimensional maps. periodic critical orbit. periodic objects. periodic orbits. perturbations. polynomials. postcritically finite maps. projective space. pushforwards. quadratic differentials. quadratic dynatomic curves. quadratic polynomials. random walks. rational maps. renormalization theory. resurgence theory. rigidity. robustness. singularly perturbed rational maps. smoothness. spherical geometry. summability condition. summable critical points. topological entropy. topological polynomials. topological space. transversality theory. tricorn. unbounded hyperbolic components. unicritical polynomial maps. unimodal interval map. unmating. Abate, Marco, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Arizzi, Marco, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Blokh, Alexander, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Bousch, Thierry, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Bu, Xavier, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Cantat, Serge, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Devaney, Robert L., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Dezotti, Alexandre, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Dinh, Tien-Cuong, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Dujardin, Romain, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb García-Compeán, Hugo, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Goldman, William M., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Grigorchuk, Rostislav, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Hubbard, John Hamal, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Jiang, Yunping, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Kiwi, Jan, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Lei, Tan, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Levin, Genadi, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Lyubich, Misha, author. aut http://id.loc.gov/vocabulary/relators/aut Meyer, Daniel, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Milnor, John, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Moreira, Carlos Gustavo, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Muñoz, Vicente, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Nguyên, Viet-Anh, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Oversteegen, Lex, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Ptacek, Ross, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Pérez-Marco, Ricardo, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Raissy, Jasmin, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Roesch, Pascale, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Santos-Silva, Roberto, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Schleicher, Dierk, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Sibony, Nessim, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Smania, Daniel, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Strien, Sebastian van, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Sutherland, Scott, author. aut http://id.loc.gov/vocabulary/relators/aut Thurston, William P., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Timorin, Vladlen, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Verjovsky, Alberto, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package 9783110501063 ZDB-23-PMS Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 9783110665925 print 9780691159294 https://doi.org/10.1515/9781400851317?locatt=mode:legacy https://www.degruyter.com/isbn/9781400851317 Cover https://www.degruyter.com/document/cover/isbn/9781400851317/original |
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English |
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Bonifant, Araceli, Bonifant, Araceli, Lyubich, Misha, Sutherland, Scott, |
spellingShingle |
Bonifant, Araceli, Bonifant, Araceli, Lyubich, Misha, Sutherland, Scott, Frontiers in Complex Dynamics : In Celebration of John Milnor's 80th Birthday (PMS-51) / Princeton Mathematical Series Frontmatter -- Contents -- Preface -- Introduction -- Part I. One Complex Variable -- Arithmetic of Unicritical Polynomial Maps -- Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques -- Dynamical cores of topological polynomials -- The quadratic dynatomic curves are smooth and irreducible -- Multicorns are not path connected -- Leading monomials of escape regions -- Limiting behavior of Julia sets of singularly perturbed rational maps -- On (non-)local connectivity of some Julia sets -- Perturbations of weakly expanding critical orbits -- Unmating of rational maps: Sufficient criteria and examples -- A framework toward understanding the characterization of holomorphic dynamics -- Part II. One Real Variable -- Metric stability for random walks (with applications in renormalization theory) -- Milnor's conjecture on monotonicity of topological entropy: Results and questions -- Entropy in dimension one -- Part III. Several Complex Variables -- On Écalle-Hakim's theorems in holomorphic dynamics -- Index theorems for meromorphic self-maps of the projective space -- Dynamics of automorphisms of compact complex surfaces -- Bifurcation currents and equidistribution in parameter space -- Part IV. Laminations and Foliations -- Entropy for hyperbolic Riemann surface laminations I -- Entropy for hyperbolic Riemann surface laminations II -- Intersection theory for ergodic solenoids -- Invariants of four-manifolds with flows via cohomological field theory -- Color Plates -- Part V. Geometry and Algebra -- Two papers which changed my life: Milnor's seminal work on at manifolds and bundles -- Milnor's problem on the growth of groups and its consequences -- Contributors -- Index |
author_facet |
Bonifant, Araceli, Bonifant, Araceli, Lyubich, Misha, Sutherland, Scott, Abate, Marco, Abate, Marco, Arizzi, Marco, Arizzi, Marco, Blokh, Alexander, Blokh, Alexander, Bousch, Thierry, Bousch, Thierry, Bu, Xavier, Bu, Xavier, Cantat, Serge, Cantat, Serge, Devaney, Robert L., Devaney, Robert L., Dezotti, Alexandre, Dezotti, Alexandre, Dinh, Tien-Cuong, Dinh, Tien-Cuong, Dujardin, Romain, Dujardin, Romain, García-Compeán, Hugo, García-Compeán, Hugo, Goldman, William M., Goldman, William M., Grigorchuk, Rostislav, Grigorchuk, Rostislav, Hubbard, John Hamal, Hubbard, John Hamal, Jiang, Yunping, Jiang, Yunping, Kiwi, Jan, Kiwi, Jan, Lei, Tan, Lei, Tan, Levin, Genadi, Levin, Genadi, Lyubich, Misha, Lyubich, Misha, Meyer, Daniel, Meyer, Daniel, Milnor, John, Milnor, John, Moreira, Carlos Gustavo, Moreira, Carlos Gustavo, Muñoz, Vicente, Muñoz, Vicente, Nguyên, Viet-Anh, Nguyên, Viet-Anh, Oversteegen, Lex, Oversteegen, Lex, Ptacek, Ross, Ptacek, Ross, Pérez-Marco, Ricardo, Pérez-Marco, Ricardo, Raissy, Jasmin, Raissy, Jasmin, Roesch, Pascale, Roesch, Pascale, Santos-Silva, Roberto, Santos-Silva, Roberto, Schleicher, Dierk, Schleicher, Dierk, Sibony, Nessim, Sibony, Nessim, Smania, Daniel, Smania, Daniel, Strien, Sebastian van, Strien, Sebastian van, Sutherland, Scott, Sutherland, Scott, Thurston, William P., Thurston, William P., Timorin, Vladlen, Timorin, Vladlen, Verjovsky, Alberto, Verjovsky, Alberto, |
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Abate, Marco, Abate, Marco, Arizzi, Marco, Arizzi, Marco, Blokh, Alexander, Blokh, Alexander, Bousch, Thierry, Bousch, Thierry, Bu, Xavier, Bu, Xavier, Cantat, Serge, Cantat, Serge, Devaney, Robert L., Devaney, Robert L., Dezotti, Alexandre, Dezotti, Alexandre, Dinh, Tien-Cuong, Dinh, Tien-Cuong, Dujardin, Romain, Dujardin, Romain, García-Compeán, Hugo, García-Compeán, Hugo, Goldman, William M., Goldman, William M., Grigorchuk, Rostislav, Grigorchuk, Rostislav, Hubbard, John Hamal, Hubbard, John Hamal, Jiang, Yunping, Jiang, Yunping, Kiwi, Jan, Kiwi, Jan, Lei, Tan, Lei, Tan, Levin, Genadi, Levin, Genadi, Lyubich, Misha, Lyubich, Misha, Meyer, Daniel, Meyer, Daniel, Milnor, John, Milnor, John, Moreira, Carlos Gustavo, Moreira, Carlos Gustavo, Muñoz, Vicente, Muñoz, Vicente, Nguyên, Viet-Anh, Nguyên, Viet-Anh, Oversteegen, Lex, Oversteegen, Lex, Ptacek, Ross, Ptacek, Ross, Pérez-Marco, Ricardo, Pérez-Marco, Ricardo, Raissy, Jasmin, Raissy, Jasmin, Roesch, Pascale, Roesch, Pascale, Santos-Silva, Roberto, Santos-Silva, Roberto, Schleicher, Dierk, Schleicher, Dierk, Sibony, Nessim, Sibony, Nessim, Smania, Daniel, Smania, Daniel, Strien, Sebastian van, Strien, Sebastian van, Sutherland, Scott, Sutherland, Scott, Thurston, William P., Thurston, William P., Timorin, Vladlen, Timorin, Vladlen, Verjovsky, Alberto, Verjovsky, Alberto, |
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author_sort |
Bonifant, Araceli, |
title |
Frontiers in Complex Dynamics : In Celebration of John Milnor's 80th Birthday (PMS-51) / |
title_sub |
In Celebration of John Milnor's 80th Birthday (PMS-51) / |
title_full |
Frontiers in Complex Dynamics : In Celebration of John Milnor's 80th Birthday (PMS-51) / Araceli Bonifant, Scott Sutherland, Misha Lyubich. |
title_fullStr |
Frontiers in Complex Dynamics : In Celebration of John Milnor's 80th Birthday (PMS-51) / Araceli Bonifant, Scott Sutherland, Misha Lyubich. |
title_full_unstemmed |
Frontiers in Complex Dynamics : In Celebration of John Milnor's 80th Birthday (PMS-51) / Araceli Bonifant, Scott Sutherland, Misha Lyubich. |
title_auth |
Frontiers in Complex Dynamics : In Celebration of John Milnor's 80th Birthday (PMS-51) / |
title_alt |
Frontmatter -- Contents -- Preface -- Introduction -- Part I. One Complex Variable -- Arithmetic of Unicritical Polynomial Maps -- Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques -- Dynamical cores of topological polynomials -- The quadratic dynatomic curves are smooth and irreducible -- Multicorns are not path connected -- Leading monomials of escape regions -- Limiting behavior of Julia sets of singularly perturbed rational maps -- On (non-)local connectivity of some Julia sets -- Perturbations of weakly expanding critical orbits -- Unmating of rational maps: Sufficient criteria and examples -- A framework toward understanding the characterization of holomorphic dynamics -- Part II. One Real Variable -- Metric stability for random walks (with applications in renormalization theory) -- Milnor's conjecture on monotonicity of topological entropy: Results and questions -- Entropy in dimension one -- Part III. Several Complex Variables -- On Écalle-Hakim's theorems in holomorphic dynamics -- Index theorems for meromorphic self-maps of the projective space -- Dynamics of automorphisms of compact complex surfaces -- Bifurcation currents and equidistribution in parameter space -- Part IV. Laminations and Foliations -- Entropy for hyperbolic Riemann surface laminations I -- Entropy for hyperbolic Riemann surface laminations II -- Intersection theory for ergodic solenoids -- Invariants of four-manifolds with flows via cohomological field theory -- Color Plates -- Part V. Geometry and Algebra -- Two papers which changed my life: Milnor's seminal work on at manifolds and bundles -- Milnor's problem on the growth of groups and its consequences -- Contributors -- Index |
title_new |
Frontiers in Complex Dynamics : |
title_sort |
frontiers in complex dynamics : in celebration of john milnor's 80th birthday (pms-51) / |
series |
Princeton Mathematical Series |
series2 |
Princeton Mathematical Series |
publisher |
Princeton University Press, |
publishDate |
2014 |
physical |
1 online resource (800 p.) : 32 color illus. Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Introduction -- Part I. One Complex Variable -- Arithmetic of Unicritical Polynomial Maps -- Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques -- Dynamical cores of topological polynomials -- The quadratic dynatomic curves are smooth and irreducible -- Multicorns are not path connected -- Leading monomials of escape regions -- Limiting behavior of Julia sets of singularly perturbed rational maps -- On (non-)local connectivity of some Julia sets -- Perturbations of weakly expanding critical orbits -- Unmating of rational maps: Sufficient criteria and examples -- A framework toward understanding the characterization of holomorphic dynamics -- Part II. One Real Variable -- Metric stability for random walks (with applications in renormalization theory) -- Milnor's conjecture on monotonicity of topological entropy: Results and questions -- Entropy in dimension one -- Part III. Several Complex Variables -- On Écalle-Hakim's theorems in holomorphic dynamics -- Index theorems for meromorphic self-maps of the projective space -- Dynamics of automorphisms of compact complex surfaces -- Bifurcation currents and equidistribution in parameter space -- Part IV. Laminations and Foliations -- Entropy for hyperbolic Riemann surface laminations I -- Entropy for hyperbolic Riemann surface laminations II -- Intersection theory for ergodic solenoids -- Invariants of four-manifolds with flows via cohomological field theory -- Color Plates -- Part V. Geometry and Algebra -- Two papers which changed my life: Milnor's seminal work on at manifolds and bundles -- Milnor's problem on the growth of groups and its consequences -- Contributors -- Index |
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9781400851317 9783110501063 9783110665925 9780691159294 |
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Q - Science |
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QA - Mathematics |
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QA614 |
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QA 3614.8 |
url |
https://doi.org/10.1515/9781400851317?locatt=mode:legacy https://www.degruyter.com/isbn/9781400851317 https://www.degruyter.com/document/cover/isbn/9781400851317/original |
illustrated |
Illustrated |
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500 - Science |
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510 - Mathematics |
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515 - Analysis |
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515.39 |
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3515.39 |
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515.39 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>13433nam a22024135i 4500</leader><controlfield tag="001">9781400851317</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20220131112047.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">220131t20142014nju fo d z eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400851317</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400851317</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)453975</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)979630037</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">nju</subfield><subfield code="c">US-NJ</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA614.8</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT036000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">515.39</subfield><subfield code="2">23</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Bonifant, Araceli, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Frontiers in Complex Dynamics :</subfield><subfield code="b">In Celebration of John Milnor's 80th Birthday (PMS-51) /</subfield><subfield code="c">Araceli Bonifant, Scott Sutherland, Misha Lyubich.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Course Book</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ : </subfield><subfield code="b">Princeton University Press, </subfield><subfield code="c">[2014]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2014</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (800 p.) :</subfield><subfield code="b">32 color illus.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Princeton Mathematical Series</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Introduction -- </subfield><subfield code="t">Part I. One Complex Variable -- </subfield><subfield code="t">Arithmetic of Unicritical Polynomial Maps -- </subfield><subfield code="t">Les racines des composantes hyperboliques de M sont des quarts d'entiers algébriques -- </subfield><subfield code="t">Dynamical cores of topological polynomials -- </subfield><subfield code="t">The quadratic dynatomic curves are smooth and irreducible -- </subfield><subfield code="t">Multicorns are not path connected -- </subfield><subfield code="t">Leading monomials of escape regions -- </subfield><subfield code="t">Limiting behavior of Julia sets of singularly perturbed rational maps -- </subfield><subfield code="t">On (non-)local connectivity of some Julia sets -- </subfield><subfield code="t">Perturbations of weakly expanding critical orbits -- </subfield><subfield code="t">Unmating of rational maps: Sufficient criteria and examples -- </subfield><subfield code="t">A framework toward understanding the characterization of holomorphic dynamics -- </subfield><subfield code="t">Part II. One Real Variable -- </subfield><subfield code="t">Metric stability for random walks (with applications in renormalization theory) -- </subfield><subfield code="t">Milnor's conjecture on monotonicity of topological entropy: Results and questions -- </subfield><subfield code="t">Entropy in dimension one -- </subfield><subfield code="t">Part III. Several Complex Variables -- </subfield><subfield code="t">On Écalle-Hakim's theorems in holomorphic dynamics -- </subfield><subfield code="t">Index theorems for meromorphic self-maps of the projective space -- </subfield><subfield code="t">Dynamics of automorphisms of compact complex surfaces -- </subfield><subfield code="t">Bifurcation currents and equidistribution in parameter space -- </subfield><subfield code="t">Part IV. Laminations and Foliations -- </subfield><subfield code="t">Entropy for hyperbolic Riemann surface laminations I -- </subfield><subfield code="t">Entropy for hyperbolic Riemann surface laminations II -- </subfield><subfield code="t">Intersection theory for ergodic solenoids -- </subfield><subfield code="t">Invariants of four-manifolds with flows via cohomological field theory -- </subfield><subfield code="t">Color Plates -- </subfield><subfield code="t">Part V. Geometry and Algebra -- </subfield><subfield code="t">Two papers which changed my life: Milnor's seminal work on at manifolds and bundles -- </subfield><subfield code="t">Milnor's problem on the growth of groups and its consequences -- </subfield><subfield code="t">Contributors -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing. This collection will be useful to students and researchers for decades to come. The contributors are Marco Abate, Marco Arizzi, Alexander Blokh, Thierry Bousch, Xavier Buff, Serge Cantat, Tao Chen, Robert Devaney, Alexandre Dezotti, Tien-Cuong Dinh, Romain Dujardin, Hugo García-Compeán, William Goldman, Rotislav Grigorchuk, John Hubbard, Yunping Jiang, Linda Keen, Jan Kiwi, Genadi Levin, Daniel Meyer, John Milnor, Carlos Moreira, Vincente Muñoz, Viet-Anh Nguyên, Lex Oversteegen, Ricardo Pérez-Marco, Ross Ptacek, Jasmin Raissy, Pascale Roesch, Roberto Santos-Silva, Dierk Schleicher, Nessim Sibony, Daniel Smania, Tan Lei, William Thurston, Vladlen Timorin, Sebastian van Strien, and Alberto Verjovsky.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Differentiable dynamical systems.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Dynamics.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Functions of complex variables.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Combinatorics.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">John Milnor.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Jordan curves.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Julia sets.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">K-theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">M. Hakim.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Maldelbrot set.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Milnor's conjecture.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sierpinski carpets.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sierpinski gaskets.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Thurston Rigidity Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">William Thurston.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">antiholomorphic quadratic polynomials.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">antiholomorphic unicritical polynomials.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">arithmetics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">asymptotic behavior.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">automorphisms.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">biholomorphisms.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">combinatorial group theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">complex manifolds.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">complex polynomials.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">conformal distortion.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">conjugacy.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">connectedness loci.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">critical objects.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">critical point.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">critically finite case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">decomposition.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">differential geometry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">differential topology.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">dynamical cores.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">dynamical derivatives.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">dynamical scales.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">dynamical systems.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">dynamics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">eigenvalues.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">entropy theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">entropy.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">escape regions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">expanding critical orbits.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">external rays.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">geometrically finite rational maps.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">global meromorphic maps.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">holomorphic dynamics studies.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">holomorphic dynamics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">holomorphic germs.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">holomorphic maps.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">hyperbolic distortion.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">hyperbolic geometry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">hyperbolicity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">identity germ.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">implosions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">index theorems.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">infinitely renormalizable quadratic polynomials.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">integral closure.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">interval dynamics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">irreducibility.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">kneading sequences.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">laminations.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">leading monomial vector.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">leading monomials.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">limiting behavior.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">local connectivity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">local dynamics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">mathematics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">mating.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">metric stability.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">monotonicity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">multicorn.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">non-locally connected Julia sets.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">one-dimensional maps.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">periodic critical orbit.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">periodic objects.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">periodic orbits.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">perturbations.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">polynomials.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">postcritically finite maps.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">projective space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">pushforwards.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">quadratic differentials.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">quadratic dynatomic curves.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">quadratic polynomials.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">random walks.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">rational maps.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">renormalization theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">resurgence theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">rigidity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">robustness.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">singularly perturbed rational maps.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">smoothness.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">spherical geometry.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">summability condition.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">summable critical points.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">topological entropy.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">topological polynomials.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">topological space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">transversality theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">tricorn.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">unbounded hyperbolic components.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">unicritical polynomial maps.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">unimodal interval map.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">unmating.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Abate, Marco, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Arizzi, Marco, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Blokh, Alexander, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bousch, Thierry, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Bu, Xavier, </subfield><subfield code="e">contributor.</subfield><subfield code="4">ctb</subfield><subfield code="4">https://id.loc.gov/vocabulary/relators/ctb</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Cantat, Serge, </subfield><subfield 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