English

Centralizers of C^1-generic diffeomorphisms

Dynamical Systems 2007-05-23 v1

Abstract

On the one hand, we prove that the spaces of C^1 symplectomorphisms and of C^1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On the other hand, we show that the space of C^1 diffeomorphisms of the circle and a non-empty open set of C^1 diffeomorphisms of the two-sphere contain dense subsets of diffeomorphisms whose centralizer has a sub-group isomorphic to R.

Keywords

Cite

@article{arxiv.math/0610064,
  title  = {Centralizers of C^1-generic diffeomorphisms},
  author = {Christian Bonatti and Sylvain Crovisier and Amie Wilkinson},
  journal= {arXiv preprint arXiv:math/0610064},
  year   = {2007}
}