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Perturbation de la Dynamique de Difféomorphismes en Topologie \(C^1\)
Sylvain Crovisier, University of Paris-Sud, Orsay, France
A publication of the Société Mathématique de France.
cover
Astérisque
2013; 164 pp; softcover
Number: 354
ISBN-13: 978-2-85629-764-3
List Price: US$67
Member Price: US$53.60
Order Code: AST/354
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This memoir deals with the dynamics of diffeomorphisms of compact manifolds. For the study of generic properties or for the construction of examples, it is often useful to be able to perturb a system. This generally leads to delicate problems: a local modification of the dynamics may cause a radical change in the behavior of the orbits. For the \(C^1\) topology, the author proposes various techniques which allow perturbation while controlling the dynamic: putting in transversal position, connection of orbits, perturbation of the tangent dynamics,... The author derives various applications to the description of \(C^1\)-generic diffeomorphisms.

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 diffeomorphisms.

Table of Contents

  • Introduction
  • Décomposition de la dynamique
  • Techniques de perturbation, généricité
  • Connexions de pseudo-orbites
  • Connexions globales
  • Hyperbolicité non uniforme
  • Réduction de la dimension ambiante
  • Bifurcations de points périodiques
  • Points périodiques homocliniquement liés
  • Dynamique loin des tangences homoclines : modèles centraux
  • Hyperbolicités topologique et uniforme
  • A. Centralisateurs de difféomorphismes
  • Bibliographie
  • Index
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