Birth of homoclinic intersections: a model for the central dynamics of partially hyperbolic systems

Sylvain Crovisier

doi:http://doi.org/10.4007/annals.2010.172.1641

Birth of homoclinic intersections: a model for the central dynamics of partially hyperbolic systems

Pages 1641-1677 from Volume 172 (2010), Issue 3 by Sylvain Crovisier

Abstract

We prove a conjecture of J. Palis: Any diffeomorphism of a compact manifold can be $C^1$-approximated by a Morse-Smale diffeomorphism or by a diffeomorphism having a transverse homoclinic intersection.

Keywords

Homoclinic orbit, Morse-Smale diffeomorphism, generic dynamics, homoclinic class, hyperbolic diffeomorphism, partial hyperbolicity

Mathematical Subject Classification

Primary 2000: 37B40, 37C05, 37C20, 37C29, 37C50

DOI

https://doi.org/http://doi.org/10.4007/annals.2010.172.1641

2726096

zbMATH

05850184

Milestones

Received: 16 May 2006
Accepted: 7 January 2010
Published online: 5 October 2010

Authors

Sylvain Crovisier

CNRS - Laboratoire Analyse, Géométrie et Applications
UMR 7539
Institut Galilée, Université Paris 13
Avenue J.-B. Clément, 93430
Villetaneuse
France