Complex Dynamics and Renormalization (AM-135), Volume 135 / / Curtis T. McMullen.
Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely reno...
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| Year of Publication: | 2016 |
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McMullen, Curtis T., author. aut http://id.loc.gov/vocabulary/relators/aut Complex Dynamics and Renormalization (AM-135), Volume 135 / Curtis T. McMullen. Princeton, NJ : Princeton University Press, [2016] ©1995 1 online resource (214 p.) : 31 line drawings text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 135 Frontmatter -- Contents -- Chapter 1. Introduction -- Chapter 2. Background in conformal geometry -- Chapter 3. Dynamics of rational maps -- Chapter 4. Holomorphic motions and the Mandelbrot set -- Chapter 5. Compactness in holomorphic dynamics -- Chapter 6. Polynomials and external rays -- Chapter 7. Renormalization -- Chapter 8. Puzzles and infinite renormalization -- Chapter 9. Robustness -- Chapter 10. Limits of renormalization -- Chapter 11. Real quadratic polynomials -- Appendix A. Orbifolds -- Appendix B. A closing lemma for rational maps -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps. 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) Dynamics. Mathematical physics. Polynomials. Renormalization (Physics). MATHEMATICS / Geometry / Non-Euclidean. bisacsh Analytic function. Attractor. Automorphism. Bernhard Riemann. Bounded set. Branched covering. Cantor set. Cardioid. Chain rule. Coefficient. Combinatorics. Complex manifold. Complex plane. Complex torus. Conformal geometry. Conformal map. Conjecture. Connected space. Covering space. Cyclic group. Degeneracy (mathematics). Dense set. Diagram (category theory). Diameter. Differential geometry of surfaces. Dihedral group. Dimension (vector space). Dimension. Disjoint sets. Disk (mathematics). Dynamical system. Endomorphism. Equivalence class. Equivalence relation. Ergodic theory. Euler characteristic. Filled Julia set. Geometric function theory. Geometry. Hausdorff dimension. Holomorphic function. Homeomorphism. Homology (mathematics). Hyperbolic geometry. Implicit function theorem. Injective function. Integer matrix. Interval (mathematics). Inverse limit. Julia set. Kleinian group. Limit point. Limit set. Linear map. Mandelbrot set. Manifold. Markov partition. Mathematical induction. Maxima and minima. Measure (mathematics). Moduli (physics). Monic polynomial. Montel's theorem. Möbius transformation. Natural number. Open set. Orbifold. Periodic point. Permutation. Point at infinity. Pole (complex analysis). Polynomial. Proper map. Quadratic differential. Quadratic function. Quadratic. Quasi-isometry. Quasiconformal mapping. Quotient space (topology). Removable singularity. Renormalization. Riemann mapping theorem. Riemann sphere. Riemann surface. Rigidity theory (physics). Scalar (physics). Schwarz lemma. Scientific notation. Special case. Structural stability. Subgroup. Subsequence. Symbolic dynamics. Tangent space. Theorem. Uniformization theorem. Uniformization. Union (set theory). Unit disk. Upper and lower bounds. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691029818 https://doi.org/10.1515/9781400882557 https://www.degruyter.com/isbn/9781400882557 Cover https://www.degruyter.com/document/cover/isbn/9781400882557/original |
| language |
English |
| format |
eBook |
| author |
McMullen, Curtis T., McMullen, Curtis T., |
| spellingShingle |
McMullen, Curtis T., McMullen, Curtis T., Complex Dynamics and Renormalization (AM-135), Volume 135 / Annals of Mathematics Studies ; Frontmatter -- Contents -- Chapter 1. Introduction -- Chapter 2. Background in conformal geometry -- Chapter 3. Dynamics of rational maps -- Chapter 4. Holomorphic motions and the Mandelbrot set -- Chapter 5. Compactness in holomorphic dynamics -- Chapter 6. Polynomials and external rays -- Chapter 7. Renormalization -- Chapter 8. Puzzles and infinite renormalization -- Chapter 9. Robustness -- Chapter 10. Limits of renormalization -- Chapter 11. Real quadratic polynomials -- Appendix A. Orbifolds -- Appendix B. A closing lemma for rational maps -- Bibliography -- Index |
| author_facet |
McMullen, Curtis T., McMullen, Curtis T., |
| author_variant |
c t m ct ctm c t m ct ctm |
| author_role |
VerfasserIn VerfasserIn |
| author_sort |
McMullen, Curtis T., |
| title |
Complex Dynamics and Renormalization (AM-135), Volume 135 / |
| title_full |
Complex Dynamics and Renormalization (AM-135), Volume 135 / Curtis T. McMullen. |
| title_fullStr |
Complex Dynamics and Renormalization (AM-135), Volume 135 / Curtis T. McMullen. |
| title_full_unstemmed |
Complex Dynamics and Renormalization (AM-135), Volume 135 / Curtis T. McMullen. |
| title_auth |
Complex Dynamics and Renormalization (AM-135), Volume 135 / |
| title_alt |
Frontmatter -- Contents -- Chapter 1. Introduction -- Chapter 2. Background in conformal geometry -- Chapter 3. Dynamics of rational maps -- Chapter 4. Holomorphic motions and the Mandelbrot set -- Chapter 5. Compactness in holomorphic dynamics -- Chapter 6. Polynomials and external rays -- Chapter 7. Renormalization -- Chapter 8. Puzzles and infinite renormalization -- Chapter 9. Robustness -- Chapter 10. Limits of renormalization -- Chapter 11. Real quadratic polynomials -- Appendix A. Orbifolds -- Appendix B. A closing lemma for rational maps -- Bibliography -- Index |
| title_new |
Complex Dynamics and Renormalization (AM-135), Volume 135 / |
| title_sort |
complex dynamics and renormalization (am-135), volume 135 / |
| series |
Annals of Mathematics Studies ; |
| series2 |
Annals of Mathematics Studies ; |
| publisher |
Princeton University Press, |
| publishDate |
2016 |
| physical |
1 online resource (214 p.) : 31 line drawings Issued also in print. |
| contents |
Frontmatter -- Contents -- Chapter 1. Introduction -- Chapter 2. Background in conformal geometry -- Chapter 3. Dynamics of rational maps -- Chapter 4. Holomorphic motions and the Mandelbrot set -- Chapter 5. Compactness in holomorphic dynamics -- Chapter 6. Polynomials and external rays -- Chapter 7. Renormalization -- Chapter 8. Puzzles and infinite renormalization -- Chapter 9. Robustness -- Chapter 10. Limits of renormalization -- Chapter 11. Real quadratic polynomials -- Appendix A. Orbifolds -- Appendix B. A closing lemma for rational maps -- Bibliography -- Index |
| isbn |
9781400882557 9783110494914 9783110442496 9780691029818 |
| callnumber-first |
Q - Science |
| callnumber-subject |
QC - Physics |
| callnumber-label |
QC20 |
| callnumber-sort |
QC 220.7 R43 M36 41994EB |
| url |
https://doi.org/10.1515/9781400882557 https://www.degruyter.com/isbn/9781400882557 https://www.degruyter.com/document/cover/isbn/9781400882557/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
530 - Physics |
| dewey-ones |
530 - Physics |
| dewey-full |
530.1/43/0151 |
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3530.1 243 3151 |
| dewey-raw |
530.1/43/0151 |
| dewey-search |
530.1/43/0151 |
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10.1515/9781400882557 |
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954123972 |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
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Complex Dynamics and Renormalization (AM-135), Volume 135 / |
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