Centralizers of C^1-generic diffeomorphisms

Details Centralizers of C^1-generic diffeomorphisms Centralizers of C^1-generic diffeomorphisms

2006-10-02

arxiv.org/abs/math/0610064v1

Mathematics

Dynamical Systems

Scientific paper

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.

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