Transitivity of codimension one Anosov actions of R^k on closed manifolds

Thierry Barbot (1) , Carlos Maquera (2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 Instituto de Ciências Matemáticas e de Computação

In this paper, we define codimension one Anosov actions of $\RR^k,\ k\geq 2,$ on a closed connected orientable manifold $M$. We prove that if the ambient manifold has dimension greater than $k+2$, then the action is topologically transitive. This generalizes a result of Verjovsky for codimension one Anosov flows.

Mots clés: Anosov flow.; Anosov action; compact orbit; closing lemma; robust transitivity; Anosov flow

Domaines: Systèmes dynamiques [math.DS]

Thierry Barbot, Carlos Maquera. Transitivity of codimension one Anosov actions of R^k on closed manifolds. Ergodic Theory and Dynamical Systems, 2011, 31 (1), pp.1-22. ⟨hal-00297152v2⟩