Author 
Graczyk, Jacek.

Series 
Annals of mathematics studies ; number144 

Annals of mathematics studies ;
no. 144.

Subject 
Geodesics (Mathematics)


Mappings (Mathematics)


Polynomials.

Alt Name 
Swiatek, Grzegorz, 1964


{Acute}Swiѕtek, Grzegorz, 1964

Description 
1 online resource 
Bibliography Note 
Includes bibliographical references and 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. 
Note 
Print version record. 
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. 
Note 
In English. 
ISBN 
9781400865185 (electronic bk.) 

1400865182 (electronic bk.) 

9780691002583 

0691002576 

9780691002576 

0691002584 

9780691002583 
ISBN/ISSN 
10.1515/9781400865185 
OCLC # 
887499708 
Additional Format 
Print version: Graczyk, Jacek. Real Fatou conjecture. Princeton, N.J. : Princeton University Press, 1998 9780691002576 
