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Journal of Modern Dynamics (JMD)
 

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

Pages: 359 - 373, Issue 2, April 2008      doi:10.3934/jmd.2008.2.359

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

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.

Keywords:  Trivial centralizer, trivial symmetries, $C^1$ generic properties.
Mathematics Subject Classification:  Primary: 37C85, Secondary: 37D45.

Revised: October 2007;      Available Online: January 2008.