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**1 - 7**of**7**### Article Koszul Information Geometry and Souriau Geometric Temperature/Capacity of Lie Group Thermodynamics

, 2014

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### PRESSURES FOR GEODESIC FLOWS OF RANK ONE MANIFOLDS

"... Abstract. 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 suff ..."

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Abstract. 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 con-ditions 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. 1.