Local density of diffeomorphisms with large centralizers Densite locale des diffeomorphismes ayant un gros centralisateur

Given any compact manifold M, we construct a non-empty open subset O of the space Diff 1 (M) of C 1 -diffeomorphisms and a dense subset D ⊂ O such that the centralizer of every diffeomorphism in D is uncountable, hence non-trivial.