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C1-generic conservative diffeomorphisms have trivial centralizer

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 Added by Sylvain Crovisier
 Publication date 2007
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and research's language is English




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We prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving diffeomorphisms of connected manifolds both contain residual subsets of diffeomorphisms whose centralizers are trivial. (Les diffeomorphismes conservatifs C1-generiques ont un centralisateur trivial. Nous montrons que lespace des symplectomorphismes de classe C1 et lespace des diffeomomorphismes de classe C1 preservant une forme volume contiennent tous deux des sous-ensembles residuels de diffeomorphismes dont le centralisateur est trivial.)



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Answering a question of Smale, we prove that the space of C1 diffeomorphisms of a compact manifold contains a residual subset of diffeomorphisms whose centralizers are trivial.
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