The real Fatou conjecture / by Jacek Graczyk and Grzegorz Świa̧tek.

The real Fatou conjecture /
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Bibliographic Details
Main Authors: Graczyk, Jacek, Świa̧tek, Grzegorz, 1964- (Author)
Format: eBook
Published: Princeton, N.J. : Princeton University Press, 1998.
Series:Annals of mathematics studies ; no. 144.
Online Access:Click for online access
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
Physical Description:1 online resource
Bibliography:Includes bibliographical references and index.
Language:In English.
Source of Description, Etc. Note:Print version record.