Topological mixing of the geodesic flow on convex projective manifolds
[Mélange topologique du flot géodésique sur les variétés projectives convexes]
Blayac, Pierre-Louis1
1 2074 East Hall 530 Church Street Ann Arbor, MI 48109-1043 (USA)
Annales de l'Institut Fourier, Online first, 38 p.

Nous introduisons un sous-ensemble naturel du fibré unitaire tangent des variétés projectives convexes, appelé le fibré unitaire tangent biproximal ; il est fermé et invariant sous l’action du flot géodésique, et nous démontrons que le flot géodésique est topologiquement mélangeant dès que la variété est irréductible. Nous montrons aussi que pour les variétés projectives convexes de rang supérieur, irréductibles et compactes, le flot géodésique est topologiquement mélangeant sur chaque composante de l’ensemble non-errant.

We introduce a natural subset of the unit tangent bundle of a convex projective manifold, the biproximal unit tangent bundle; it is closed and invariant under the geodesic flow, and we prove that the geodesic flow is topologically mixing on it whenever the manifold is irreducible. We also show that, for higher-rank, irreducible, compact convex projective manifolds, the geodesic flow is topologically mixing on each connected component of the non-wandering set.

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3669
Classification : 37D40
Keywords: Convex projective manifolds, geodesic flow, topological mixing.
Mot clés : Variétés projectives convexes, flot géodésique, mélange topologique.

Blayac, Pierre-Louis 1

1 2074 East Hall 530 Church Street Ann Arbor, MI 48109-1043 (USA) 
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Blayac, Pierre-Louis. Topological mixing of the geodesic flow on convex projective manifolds. Annales de l'Institut Fourier, Online first, 38 p.

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