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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
The Real Fatou Conjecture. (Am-144), Volume 144

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

Graczyk, Jacek
Swiatek, Grzegorz

Paperback

Series: Annals of Mathematics Studies, Book 144

General MathematicsGeometry

ISBN10: 0691002584
ISBN13: 9780691002583
Publisher: Princeton Univ Pr
Published: Oct 25 1998
Pages: 148
Weight: 0.56
Height: 0.54 Width: 6.06 Depth: 9.19
Language: English

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.

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