C^1-generic conservative diffeomorphisms have trivial centralizer

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April 2008, 2(2): 359-373. doi: 10.3934/jmd.2008.2.359

$C^1$-generic conservative diffeomorphisms have trivial centralizer

Christian Bonatti ^1, , Sylvain Crovisier ^2, and Amie Wilkinson ^3,

1.	Université de Bourgogne, Laboratoire de Topologie, UMR 5584 du CNRS, BP 47 870, 21078 Dijon Cedex
2.	CNRS - Laboratoire Analyse, Géométrie et Applications UMR 7539, Institut Galilée, Université Paris 13, 99 Avenue J.-B. Clément, 934390 Villetaneuse, France
3.	Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, United States

Revised October 2007 Published January 2008

Abstract
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We prove that the spaces of $C^1$ symplectomorphisms and of $C^1$ volume-preserving diffeomorphisms of connected manifolds contain residual subsets of diffeomorphisms whose centralizers are trivial.

Keywords: Trivial centralizer, trivial symmetries, $C^1$ generic properties..

Mathematics Subject Classification: Primary: 37C85, Secondary: 37D4.

Citation: Christian Bonatti, Sylvain Crovisier, Amie Wilkinson. $C^1$-generic conservative diffeomorphisms have trivial centralizer. Journal of Modern Dynamics, 2008, 2 (2) : 359-373. doi: 10.3934/jmd.2008.2.359

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