Ergodic properties of some negatively curved manifolds with infinite measure

Pierre Vidotto

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arXiv · 1707.06056

Ergodic properties of some negatively curved manifolds with infinite measure

Pierre Vidotto

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Abstract

Let $M=X/\Gamma$ be a geometrically finite negatively curved manifold with fundamental group $\Gamma$ acting on $X$ by isometries. The purpose of this paper is to study the mixing property of the geodesic flow on $T^1M$, the asymptotic equivalent as $R\longrightarrow+\infty$ of the number of closed geodesics on $M$ of length less than $R$ and of the orbital counting function $\sharp\{\gamma\in\Gamma\ |\ d(o,\gamma.o)\le R\}$. These properties are well known when the Bowen-Margulis measure on $T^1M$ 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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Pierre Vidotto. 2017-07-19. Ergodic properties of some negatively curved manifolds with infinite measure. https://arxiv.org/abs/1707.06056

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