C1-generic conservative diffeomorphisms have trivial centralizer
Dynamical Systems
2007-10-23 v1
Abstract
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.)
Keywords
Cite
@article{arxiv.0710.3989,
title = {C1-generic conservative diffeomorphisms have trivial centralizer},
author = {Christian Bonatti and Sylvain Crovisier and Amie Wilkinson},
journal= {arXiv preprint arXiv:0710.3989},
year = {2007}
}