C1-generic conservative diffeomorphisms have trivial centralizer

Details C1-generic conservative diffeomorphisms have trivial centralizer C1-generic conservative diffeomorphisms have trivial centralizer

2007-10-22

arxiv.org/abs/0710.3989v1

Mathematics

Dynamical Systems

Scientific paper

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 diff\'eomorphismes conservatifs C1-g\'en\'eriques ont un centralisateur trivial. Nous montrons que l'espace des symplectomorphismes de classe C1 et l'espace des diff\'eomomorphismes de classe C1 pr\'eservant une forme volume contiennent tous deux des sous-ensembles r\'esiduels de diff\'eomorphismes dont le centralisateur est trivial.)

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