Home Mathematics The Real Fatou Conjecture. (AM-144), Volume 144
book: The Real Fatou Conjecture. (AM-144), Volume 144
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The Real Fatou Conjecture. (AM-144), Volume 144

  • Jacek Graczyk and Grzegorz Swiatek
Language: English
Published/Copyright: 1999
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About this book

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 / Editor information

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


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Pages and Images/Illustrations in book
eBook published on:
September 8, 2014
eBook ISBN:
9781400865185
Pages and Images/Illustrations in book
Main content:
148
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8 illus.
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