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Annales scientifiques de l’ENS, série 4 - Titles - 41 - pages 925-954

Titlessérie 4, 41

Local density of diffeomorphisms with large centralizers

Christian BONATTI, Sylvain CROVISIER, Gioia M. VAGO, Amie WILKINSON

ANNALES SCIENTIFIQUES DE L’ÉCOLE NORMALE SUPÉRIEURE, série 4, 41, fascicule 6 (2008), 925-954

Download this paper : PDF File

Résumé :

Densité locale des difféomorphismes ayant un gros centralisateur

Pour toute variété pM  compacte, de dimension quelconque, nous construisons une partie pO ⊂ Diff1(M )  non vide, ouverte dans l’espace pDiff1(M )  des pC1  -difféomorphismes de pM  , et un sous-ensemble pD ⊂ O dense en pO , constitué de difféomorphismes dont le centralisateur est non dénombrable, donc non trivial.

Mots clefs : Centralisateur trivial, symétries triviales, invariant de Mather

Abstract :

Given any compact manifold pM  , we construct a non-empty open subset pO of the space pDif f1(M )  of pC1  -diffeomorphisms and a dense subset pD ⊂ O such that the centralizer of every diffeomorphism in pD is uncountable, hence non-trivial.

Keywords : Trivial centralizer, Trivial symmetries, Mather invariant

Class. math. : 37C85, 37C80, 37D45, 37D15, 37E30


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