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Author Graczyk, Jacek.

Title The real Fatou conjecture / by Jacek Graczyk and Grzegorz Świa̧tek
Published Princeton, N.J. : Princeton University Press, 1998
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Description 1 online resource
Series Annals of mathematics studies ; number144
Annals of mathematics studies ; no. 144
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
Summary 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
Bibliography Includes bibliographical references and index
Notes In English
Print version record
Subject Geodesics (Mathematics)
Mappings (Mathematics)
Polynomials.
Form Electronic book
Author Świa̧tek, Grzegorz, 1964-
ISBN 1400865182 (electronic bk.)
9781400865185 (electronic bk.)