The Real Fatou Conjecture. (AM-144), Volume 144 / / Grzegorz Swiatek, Jacek Graczyk.
In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it c...
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Graczyk, Jacek, author. aut http://id.loc.gov/vocabulary/relators/aut The Real Fatou Conjecture. (AM-144), Volume 144 / Grzegorz Swiatek, Jacek Graczyk. Princeton, NJ : Princeton University Press, [2014] ©1999 1 online resource (148 p.) : 8 illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 144 Frontmatter -- Contents -- Chapter 1. Review of Concepts -- Chapter 2. Quasiconformal Gluing -- Chapter 3. Polynomial-Like Property -- Chapter 4. Linear Growth of Moduli -- Chapter 5. Quasi conformal Techniques -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star In 1920, Pierre Fatou expressed the conjecture that--except for special cases--all critical points of a rational map of the Riemann sphere tend to periodic orbits under iteration. This conjecture remains the main open problem in the dynamics of iterated maps. For the logistic family x- ax(1-x), it can be interpreted to mean that for a dense set of parameters "a," an attracting periodic orbit exists. The same question appears naturally in science, where the logistic family is used to construct models in physics, ecology, and economics. In this book, Jacek Graczyk and Grzegorz Swiatek provide a rigorous proof of the Real Fatou Conjecture. In spite of the apparently elementary nature of the problem, its solution requires advanced tools of complex analysis. The authors have written a self-contained and complete version of the argument, accessible to someone with no knowledge of complex dynamics and only basic familiarity with interval maps. The book will thus be useful to specialists in real dynamics as well as to graduate students. 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) MATHEMATICS / Geometry / Non-Euclidean. bisacsh Absolute value. Affine transformation. Algebraic function. Analytic continuation. Analytic function. Arithmetic. Automorphism. Big O notation. Bounded set (topological vector space). C0. Calculation. Canonical map. Change of variables. Chebyshev polynomials. Combinatorics. Commutative property. Complex number. Complex plane. Complex quadratic polynomial. Conformal map. Conjecture. Conjugacy class. Conjugate points. Connected component (graph theory). Connected space. Continuous function. Corollary. Covering space. Critical point (mathematics). Dense set. Derivative. Diffeomorphism. Dimension. Disjoint sets. Disjoint union. Disk (mathematics). Equicontinuity. Estimation. Existential quantification. Fibonacci. Functional equation. Fundamental domain. Generalization. Great-circle distance. Hausdorff distance. Holomorphic function. Homeomorphism. Homotopy. Hyperbolic function. Imaginary number. Implicit function theorem. Injective function. Integer. Intermediate value theorem. Interval (mathematics). Inverse function. Irreducible polynomial. Iteration. Jordan curve theorem. Julia set. Limit of a sequence. Linear map. Local diffeomorphism. Mathematical induction. Mathematical proof. Maxima and minima. Meromorphic function. Moduli (physics). Monomial. Monotonic function. Natural number. Neighbourhood (mathematics). Open set. Parameter. Periodic function. Periodic point. Phase space. Point at infinity. Polynomial. Projection (mathematics). Quadratic function. Quadratic. Quasiconformal mapping. Renormalization. Riemann sphere. Riemann surface. Schwarzian derivative. Scientific notation. Subsequence. Theorem. Theory. Topological conjugacy. Topological entropy. Topology. Union (set theory). Unit circle. Unit disk. Upper and lower bounds. Upper half-plane. Z0. Swiatek, Grzegorz, author. aut http://id.loc.gov/vocabulary/relators/aut 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 9780691002583 https://doi.org/10.1515/9781400865185 https://www.degruyter.com/isbn/9781400865185 Cover https://www.degruyter.com/document/cover/isbn/9781400865185/original |
| language |
English |
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eBook |
| author |
Graczyk, Jacek, Graczyk, Jacek, Swiatek, Grzegorz, |
| spellingShingle |
Graczyk, Jacek, Graczyk, Jacek, Swiatek, Grzegorz, The Real Fatou Conjecture. (AM-144), Volume 144 / Annals of Mathematics Studies ; Frontmatter -- Contents -- Chapter 1. Review of Concepts -- Chapter 2. Quasiconformal Gluing -- Chapter 3. Polynomial-Like Property -- Chapter 4. Linear Growth of Moduli -- Chapter 5. Quasi conformal Techniques -- Bibliography -- Index |
| author_facet |
Graczyk, Jacek, Graczyk, Jacek, Swiatek, Grzegorz, Swiatek, Grzegorz, Swiatek, Grzegorz, |
| author_variant |
j g jg j g jg g s gs |
| author_role |
VerfasserIn VerfasserIn VerfasserIn |
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Swiatek, Grzegorz, Swiatek, Grzegorz, |
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Graczyk, Jacek, |
| title |
The Real Fatou Conjecture. (AM-144), Volume 144 / |
| title_full |
The Real Fatou Conjecture. (AM-144), Volume 144 / Grzegorz Swiatek, Jacek Graczyk. |
| title_fullStr |
The Real Fatou Conjecture. (AM-144), Volume 144 / Grzegorz Swiatek, Jacek Graczyk. |
| title_full_unstemmed |
The Real Fatou Conjecture. (AM-144), Volume 144 / Grzegorz Swiatek, Jacek Graczyk. |
| title_auth |
The Real Fatou Conjecture. (AM-144), Volume 144 / |
| title_alt |
Frontmatter -- Contents -- Chapter 1. Review of Concepts -- Chapter 2. Quasiconformal Gluing -- Chapter 3. Polynomial-Like Property -- Chapter 4. Linear Growth of Moduli -- Chapter 5. Quasi conformal Techniques -- Bibliography -- Index |
| title_new |
The Real Fatou Conjecture. (AM-144), Volume 144 / |
| title_sort |
the real fatou conjecture. (am-144), volume 144 / |
| series |
Annals of Mathematics Studies ; |
| series2 |
Annals of Mathematics Studies ; |
| publisher |
Princeton University Press, |
| publishDate |
2014 |
| physical |
1 online resource (148 p.) : 8 illus. Issued also in print. |
| contents |
Frontmatter -- Contents -- Chapter 1. Review of Concepts -- Chapter 2. Quasiconformal Gluing -- Chapter 3. Polynomial-Like Property -- Chapter 4. Linear Growth of Moduli -- Chapter 5. Quasi conformal Techniques -- Bibliography -- Index |
| isbn |
9781400865185 9783110494914 9783110442496 9780691002583 |
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Q - Science |
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QA - Mathematics |
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QA614 |
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QA 3614.58 G73 42014 |
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https://doi.org/10.1515/9781400865185 https://www.degruyter.com/isbn/9781400865185 https://www.degruyter.com/document/cover/isbn/9781400865185/original |
| illustrated |
Illustrated |
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500 - Science |
| dewey-tens |
510 - Mathematics |
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516 - Geometry |
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516.362 |
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3516.362 |
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516.362 |
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516.362 |
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10.1515/9781400865185 |
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887499708 |
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