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About this product
- DescriptionIn 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 ecomics. 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 kwledge 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(s)Grzegorz Swiatek,Jacek Graczyk
- PublisherPrinceton University Press
- Date of Publication05/10/1998
- Series TitleAnnals of Mathematics Studies
- Series Part/Volume Numberv. 144
- Place of PublicationNew Jersey
- Country of PublicationUnited States
- ImprintPrinceton University Press
- Content Note8 illus.
- Weight228 g
- Width152 mm
- Height229 mm
- Spine8 mm
- Format DetailsTrade paperback (US)
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