Local density of diffeomorphisms with large centralizers
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 6, pp. 925-954.

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 𝒟𝒪 such that the centralizer of every diffeomorphism in 𝒟 is uncountable, hence non-trivial.

Pour toute variété M compacte, de dimension quelconque, nous construisons une partie 𝒪 Diff 1 (M) non vide, ouverte dans l’espace Diff 1 (M) des C 1 -difféomorphismes de M, et un sous-ensemble 𝒟𝒪 dense en 𝒪, constitué de difféomorphismes dont le centralisateur est non dénombrable, donc non trivial.

DOI: 10.24033/asens.2085
Classification: 37C85,  37C80,  37D45,  37D15,  37E30
Keywords: trivial centralizer, trivial symmetries, Mather invariant
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Bonatti, Christian; Crovisier, Sylvain; Vago, Gioia M.; Wilkinson, Amie. Local density of diffeomorphisms with large centralizers. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 6, pp. 925-954. doi : 10.24033/asens.2085. http://www.numdam.org/articles/10.24033/asens.2085/

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