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, Tome 41 (2008), p. 925-954 / Harvested from Numdam

Résumé

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

Abstract

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

Détail

Publié le : 2008-01-01

MR 2504109 | Zbl 1163.58003 | 1 citation dans Numdam

DOI : https://doi.org/10.24033/asens.2085
Classification:  37C85,  37C80,  37D45,  37D15,  37E30
Mots clés: centralisateur trivial, symétries triviales, invariant de Mather

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