Generic measures for hyperbolic flows on non compact spaces

Yves Coudène (1) , Barbara Schapira (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

We consider the geodesic flow on a complete connected negatively curved manifold. We show that the set of invariant borel probability measures contains a dense $G_\delta$-subset consisting of ergodic measures fully supported on the non-wandering set. We also trat the case of non-positively curved manifolds and provide general tools to deal with hyperbolic systems defined on non-compact spaces.

Mots clés: Negatively curved manifolds; invariant measures

Domaines: Systèmes dynamiques [math.DS]

Yves Coudène, Barbara Schapira. Generic measures for hyperbolic flows on non compact spaces. Israel Journal of Mathematics, 2010, 179, pp.157-172. ⟨10.1007/s11856-010-0076-z⟩. ⟨hal-00163451⟩