Ergodic properties of some negatively curved manifolds with infinite measure

2017/07/19 by Vidotto, Pierre
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.06056

Abstract

Let M=X/Γ be a geometrically finite negatively curved manifold with fundamental group Γ acting on X by isometries. The purpose of this paper is to study the mixing property of the geodesic flow on T¹M, the asymptotic equivalent as R\longrightarrow+∞ of the number of closed geodesics on M of length less than R and of the orbital counting function \sharp\γ∈Γ | d(o,γ.o)≤ R\. These properties are well known when the Bowen-Margulis measure on T¹M is finite. We consider here divergent Schottky groups whose Bowen-Margulis measure is infinite and ergodic, and we precise these ergodic properties using a suitable symbolic coding.

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