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Centralizers of C^1-generic diffeomorphisms

Christian Bonatti·Sylvain Crovisier·Amie Wilkinson
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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.

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Christian Bonatti, Sylvain Crovisier, Amie Wilkinson. 2006-10-02. Centralizers of C^1-generic diffeomorphisms. https://arxiv.org/abs/math/0610064

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