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arXiv · 2303.01390

Ergodicity of the geodesic flow for groups with a contracting element

Rémi Coulon
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Abstract

In this article we investigate the dynamical properties of the geodesic flow for a proper metric space endowed with a proper action by isometries of a group with a contracting element. We show that the existence of a contracting isometry is a sufficient evidence of negative curvature to carry in this context various results borrowed from hyperbolic geometry. In particular, we extend the so-called Hopf-Tsuji-Sullivan dichotomy proving that the geodesic flow is either conservative and ergodic or dissipative.

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Rémi Coulon. 2023-03-02. Ergodicity of the geodesic flow for groups with a contracting element. https://arxiv.org/abs/2303.01390

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