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Homéomorphismes de surfaces, théorémes de la fleur de Leau-Fatou et de la variété stable
Frédéric LeRoux, Université Paris Sud, Orsay, France
A publication of the Société Mathématique de France.
Astérisque
2004; 120 pp; softcover
Number: 292
ISBN-10: 2-85629-153-8
ISBN-13: 978-2-85629-153-5
List Price: US$26
Individual Members: US$23.40
Order Code: AST/292
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This book, Dynamics of Surface Homeomorphisms, Topological Versions of Leau-Fatou Flower Theorem and Stable Manifold Theorem, shows that the study of the dynamics of a surface homeomorphism in the neighborhood of an isolated fixed point leads to the following results: If the fixed point index is greater than \(1\), a family of attractive and repulsive petals is constructed, generalizing the Leau-Fatou flower theorem in complex dynamics. If the index is less than \(1\), one gets a family of stable and unstable branches, generalizing the stable manifold theorem in differentiable hyperbolic dynamics.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in differential equations and geometry.

Table of Contents

  • Introduction
  • Présentation des résultats de dynamique locale
  • Intermède : du local au global
  • Dynamique globale : énoncé et résultats préliminaires
  • Preuve du théorème principal de dynamique globale
  • Applications en dynamique locale
  • Appendice : Théorème de Schoenflies-Homma et variantes
  • Bibliographie
  • Index
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