Dynamical Systems
Local rigidity of restrictions of Weyl chamber flows
Comptes Rendus. Mathématique, Volume 344 (2007) no. 8, pp. 503-508.

In this Note we consider examples of partially hyperbolic actions: restrictions of Weyl chamber flows on SL(n,R)/Γ (n4). 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.

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 (n4). 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.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2007.03.009
Damjanović, Danijela 1; Katok, Anatole 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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Damjanović, Danijela; Katok, Anatole. 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. http://www.numdam.org/articles/10.1016/j.crma.2007.03.009/

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