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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

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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