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The real Fatou conjecture /
The real Fatou conjecture /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
1998.
|
| Colección: | Annals of mathematics studies ;
no. 144. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | JSTOR_ocn887499708 | ||
| 003 | OCoLC | ||
| 005 | 20231005004200.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 140816s1998 nju ob 001 0 eng d | ||
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| 037 | |a 22573/ctt7680c7 |b JSTOR | ||
| 050 | 4 | |a QA614.58 |b .G73 1998eb | |
| 072 | 7 | |a MAT |x 012000 |2 bisacsh | |
| 072 | 7 | |a MAT040000 |2 bisacsh | |
| 072 | 7 | |a MAT012040 |2 bisacsh | |
| 082 | 0 | 4 | |a 516.362 |2 23 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Graczyk, Jacek. | |
| 245 | 1 | 4 | |a The real Fatou conjecture / |c by Jacek Graczyk and Grzegorz Świa̧tek. |
| 260 | |a Princeton, N.J. : |b Princeton University Press, |c 1998. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies ; |v number144 | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a 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 | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Chapter 1. Review of Concepts -- |t Chapter 2. Quasiconformal Gluing -- |t Chapter 3. Polynomial-Like Property -- |t Chapter 4. Linear Growth of Moduli -- |t Chapter 5. Quasi conformal Techniques -- |t Bibliography -- |t Index. |
| 546 | |a In English. | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 650 | 0 | |a Geodesics (Mathematics) | |
| 650 | 0 | |a Mappings (Mathematics) | |
| 650 | 0 | |a Polynomials. | |
| 650 | 4 | |a Mathematik. | |
| 650 | 6 | |a Géodésiques (Mathématiques) | |
| 650 | 6 | |a Applications (Mathématiques) | |
| 650 | 6 | |a Polynômes. | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Complex Analysis. |2 bisacsh | |
| 650 | 7 | |a Geodesics (Mathematics) |2 fast | |
| 650 | 7 | |a Mappings (Mathematics) |2 fast | |
| 650 | 7 | |a Polynomials |2 fast | |
| 653 | |a Absolute value. | ||
| 653 | |a Affine transformation. | ||
| 653 | |a Algebraic function. | ||
| 653 | |a Analytic continuation. | ||
| 653 | |a Analytic function. | ||
| 653 | |a Arithmetic. | ||
| 653 | |a Automorphism. | ||
| 653 | |a Big O notation. | ||
| 653 | |a Bounded set (topological vector space) | ||
| 653 | |a C0. | ||
| 653 | |a Calculation. | ||
| 653 | |a Canonical map. | ||
| 653 | |a Change of variables. | ||
| 653 | |a Chebyshev polynomials. | ||
| 653 | |a Combinatorics. | ||
| 653 | |a Commutative property. | ||
| 653 | |a Complex number. | ||
| 653 | |a Complex plane. | ||
| 653 | |a Complex quadratic polynomial. | ||
| 653 | |a Conformal map. | ||
| 653 | |a Conjecture. | ||
| 653 | |a Conjugacy class. | ||
| 653 | |a Conjugate points. | ||
| 653 | |a Connected component (graph theory) | ||
| 653 | |a Connected space. | ||
| 653 | |a Continuous function. | ||
| 653 | |a Corollary. | ||
| 653 | |a Covering space. | ||
| 653 | |a Critical point (mathematics) | ||
| 653 | |a Dense set. | ||
| 653 | |a Derivative. | ||
| 653 | |a Diffeomorphism. | ||
| 653 | |a Dimension. | ||
| 653 | |a Disjoint sets. | ||
| 653 | |a Disjoint union. | ||
| 653 | |a Disk (mathematics) | ||
| 653 | |a Equicontinuity. | ||
| 653 | |a Estimation. | ||
| 653 | |a Existential quantification. | ||
| 653 | |a Fibonacci. | ||
| 653 | |a Functional equation. | ||
| 653 | |a Fundamental domain. | ||
| 653 | |a Generalization. | ||
| 653 | |a Great-circle distance. | ||
| 653 | |a Hausdorff distance. | ||
| 653 | |a Holomorphic function. | ||
| 653 | |a Homeomorphism. | ||
| 653 | |a Homotopy. | ||
| 653 | |a Hyperbolic function. | ||
| 653 | |a Imaginary number. | ||
| 653 | |a Implicit function theorem. | ||
| 653 | |a Injective function. | ||
| 653 | |a Integer. | ||
| 653 | |a Intermediate value theorem. | ||
| 653 | |a Interval (mathematics) | ||
| 653 | |a Inverse function. | ||
| 653 | |a Irreducible polynomial. | ||
| 653 | |a Iteration. | ||
| 653 | |a Jordan curve theorem. | ||
| 653 | |a Julia set. | ||
| 653 | |a Limit of a sequence. | ||
| 653 | |a Linear map. | ||
| 653 | |a Local diffeomorphism. | ||
| 653 | |a Mathematical induction. | ||
| 653 | |a Mathematical proof. | ||
| 653 | |a Maxima and minima. | ||
| 653 | |a Meromorphic function. | ||
| 653 | |a Moduli (physics) | ||
| 653 | |a Monomial. | ||
| 653 | |a Monotonic function. | ||
| 653 | |a Natural number. | ||
| 653 | |a Neighbourhood (mathematics) | ||
| 653 | |a Open set. | ||
| 653 | |a Parameter. | ||
| 653 | |a Periodic function. | ||
| 653 | |a Periodic point. | ||
| 653 | |a Phase space. | ||
| 653 | |a Point at infinity. | ||
| 653 | |a Polynomial. | ||
| 653 | |a Projection (mathematics) | ||
| 653 | |a Quadratic function. | ||
| 653 | |a Quadratic. | ||
| 653 | |a Quasiconformal mapping. | ||
| 653 | |a Renormalization. | ||
| 653 | |a Riemann sphere. | ||
| 653 | |a Riemann surface. | ||
| 653 | |a Schwarzian derivative. | ||
| 653 | |a Scientific notation. | ||
| 653 | |a Subsequence. | ||
| 653 | |a Theorem. | ||
| 653 | |a Theory. | ||
| 653 | |a Topological conjugacy. | ||
| 653 | |a Topological entropy. | ||
| 653 | |a Topology. | ||
| 653 | |a Union (set theory) | ||
| 653 | |a Unit circle. | ||
| 653 | |a Unit disk. | ||
| 653 | |a Upper and lower bounds. | ||
| 653 | |a Upper half-plane. | ||
| 653 | |a Z0. | ||
| 700 | 1 | |a Świa̧tek, Grzegorz, |d 1964- |e author. | |
| 776 | 0 | 8 | |i Print version: |a Graczyk, Jacek. |t Real Fatou conjecture. |d Princeton, N.J. : Princeton University Press, 1998 |z 9780691002576 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 144. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt7zv8rh |z Texto completo |
| 880 | 1 | 4 | |6 245-00/(Q |a The real Fatou conjecture / |c by Jacek Graczyk and Grzegorz Świ©ѕtek. |
| 938 | |a YBP Library Services |b YANK |n 12033124 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis28840351 | ||
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| 938 | |a ebrary |b EBRY |n ebr10907682 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL1756204 | ||
| 938 | |a De Gruyter |b DEGR |n 9781400865185 | ||
| 994 | |a 92 |b IZTAP | ||