Local rigidity of restrictions of Weyl chamber flows

Danijela Damjanović; Anatole Katok

doi:10.1016/j.crma.2007.03.009

Dynamical Systems

Local rigidity of restrictions of Weyl chamber flows
[Rigidite locale des restrictions de flots des chambres de Weyl]

Présenté par : Étienne Ghys

Danijela Damjanović ¹ ; Anatole Katok ²

¹ Institut des hautes études scientifiques, 35, route de Chartres, 91440 Bures-sur-Yvette, France
² Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA

Comptes Rendus. Mathématique, Volume 344 (2007) no. 8, pp. 503-508.

Résumé
Abstract

Dans cette Note on étudie des exemples d'actions partiellement hyperboliques : restrictions de flots des chambres de Weyl sur la variété $SL (n, R) / Γ$ ( $n ⩾ 4$ ). Nous démontrons que, génériquement, les restrictions de rang ⩾2 sont localement rigides. Notre approche combine la géométrie des feuilletages invariants et les propriétés algébriques du groupe $SL (n, R)$ . Cette approche est aussi applicable dans la démonstration de la rigidité locale des restrictions des autres flots des chambres de Weyl.

In this Note we consider examples of partially hyperbolic actions: restrictions of Weyl chamber flows on $SL (n, R) / Γ$ ( $n ⩾ 4$ ). We show that generic restrictions of rank at least two are locally rigid. Our approach combines the geometry of the invariant foliations for the action and the algebraic properties of the group $SL (n, R)$ . The method is applicable to restrictions of Weyl chamber flows on other homogeneous spaces.

Reçu le : 2006-04-12
Accepté le : 2007-02-09
Publié le : 2007-04-15

DOI : 10.1016/j.crma.2007.03.009

Affiliations des auteurs :

Danijela Damjanović ¹ ; Anatole Katok ²

¹ Institut des hautes études scientifiques, 35, route de Chartres, 91440 Bures-sur-Yvette, France
² Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA

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     title = {Local rigidity of restrictions of {Weyl} chamber flows},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {503--508},
     publisher = {Elsevier},
     volume = {344},
     number = {8},
     year = {2007},
     doi = {10.1016/j.crma.2007.03.009},
     language = {en},
}

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Danijela Damjanović; Anatole Katok. Local rigidity of restrictions of Weyl chamber flows. Comptes Rendus. Mathématique, Volume 344 (2007) no. 8, pp. 503-508. doi : 10.1016/j.crma.2007.03.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.009/

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