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

Christian Bonatti; Sylvain Crovisier; Amie Wilkinson

doi:10.3934/jmd.2008.2.359

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2008, Volume 2, Issue 2: 359-373. Doi: 10.3934/jmd.2008.2.359

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$C^1$-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
3.
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730

Revised: September 30, 2007

Published: December 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 37C85, Secondary: 37D45.

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