# American Institute of Mathematical Sciences

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

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

 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.
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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