Christian Bonatti, Sylvain Crovisier, Amie Wilkinson
Published 2006-10-02Version 1
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.
Centralizers of partially hyperbolic diffeomorphisms in dimension 3
On the centralizer of diffeomorphisms of the half-line
Accessibility and centralizers for partially hyperbolic flows
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