Local density of diffeomorphisms with large centralizers

Bonatti, Christian; Crovisier, Sylvain; Vago, Gioia M.; Wilkinson, Amie

doi:10.24033/asens.2085

Local density of diffeomorphisms with large centralizers
[Densité locale des difféomorphismes ayant un gros centralisateur]

Bonatti, Christian ; Crovisier, Sylvain ; Vago, Gioia M. ; Wilkinson, Amie

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 41 (2008) no. 6, pp. 925-954.

Résumé
Abstract

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

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 $𝒟 \subset 𝒪$ such that the centralizer of every diffeomorphism in $𝒟$ is uncountable, hence non-trivial.

MR Zbl | 3 citations dans Numdam

DOI : 10.24033/asens.2085

Classification : 37C85, 37C80, 37D45, 37D15, 37E30
Keywords: trivial centralizer, trivial symmetries, Mather invariant
Mot clés : centralisateur trivial, symétries triviales, invariant de Mather

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     author = {Bonatti, Christian and Crovisier, Sylvain and Vago, Gioia M. and Wilkinson, Amie},
     title = {Local density of diffeomorphisms with large centralizers},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {925--954},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 41},
     number = {6},
     year = {2008},
     doi = {10.24033/asens.2085},
     mrnumber = {2504109},
     zbl = {1163.58003},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.2085/}
}

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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, Série 4, Tome 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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