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. PolynomialLike Property  Chapter 4. Linear Growth of Moduli  Chapter 5. Quasi conformal Techniques  Bibliography  Index 
Summary 
In 1920, Pierre Fatou expressed the conjecture thatexcept for special casesall 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(1x), 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 selfcontained 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.) 
