Centralizers of C1-generic diffeomorphisms
Abstract
On the one hand, we prove that the spaces of C1 symplectomorphisms and of C1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On the other hand, we show that the space of C1 diffeomorphisms of the circle and a non-empty open set of C1 diffeomorphisms of the two-sphere contain dense subsets of diffeomorphisms whose centralizer has a sub-group isomorphic to R.
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