Pressures for geodesic flows of rank one manifolds

Barbara Schapira (1, 2) , Katrin Gelfert (3)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Instituto de Matematica Universidade Federal do Rio de Janeir

We study the geodesic flow on the unit tangent bundle of a rank one manifold and we give conditions under which all classical definitions of pressure of a Hölder continuous potential coincide. We provide a large deviation statement, which allows to neglect (periodic) orbits that lack sufficient hyperbolic behavior. Our results involve conditions on the potential, that take into consideration its properties in the nonhyperbolic part of the manifold. We draw some conclusions for the construction of equilibrium states.

Mots clés: thermodynamical formalism; pressure; geodesic flow; nonpositive curvature

Domaines: Systèmes dynamiques [math.DS]

Barbara Schapira, Katrin Gelfert. Pressures for geodesic flows of rank one manifolds. Nonlinearity, 2014, 27 (7), pp.1575-1594. ⟨10.1088/0951-7715/27/7/1575⟩. ⟨hal-00881421⟩