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

Format:

Book

Author/Creator:

Graczyk, Jacek, author.

Swiatek, Grzegorz, 1964- author.

Series:

Annals of mathematics studies ; Number 144.

Annals of Mathematics Studies ; Number 144

Language:

English

Subjects (All):

Geodesics (Mathematics).

Polynomials.

Mappings (Mathematics).

Physical Description:

1 online resource (158 p.)

Edition:

1st ed.

Place of Publication:

Princeton, New Jersey : Princeton University Press, 1998.

Language Note:

English

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.

Contents:

Front matter

Contents

Chapter 1. Review of Concepts

Chapter 2. Quasiconformal Gluing

Chapter 3. Polynomial-Like Property

Chapter 4. Linear Growth of Moduli

Chapter 5. Quasi conformal Techniques

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-691-00257-6

1-4008-6518-2

OCLC:

887499708