The Real Fatou Conjecture. (AM-144), Volume 144 / / Grzegorz Swiatek, Jacek Graczyk.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Graczyk, Jacek,; Swiatek, Grzegorz,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2014]; ©1999
• Year of Publication: 2014
• Language: English
• Series: Annals of Mathematics Studies ; 144
• Physical Description: 1 online resource (148 p.) :; 8 illus.
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400865185; 9783110494914; 9783110442496
• DOI: 10.1515/9781400865185
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: 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 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.