The Real Fatou Conjecture. (Am-144), Volume 144

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.

Author: Jacek Graczyk,Grzegorz Swiatek
Publisher: Princeton University Press
Published: 10/25/1998
Pages: 148
Binding Type: Paperback
Weight: 0.56lbs
Size: 9.19h x 6.06w x 0.54d
ISBN: 9780691002583

About the Author
Jacek Graczyk is Assistant Professor of Mathematics at Michigan State University. Grzegorz Swiatek is Associate Professor of Mathematics at Pennsylvania State University.