Ergodicity of the geodesic flow for groups with a contracting element - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

Ergodicity of the geodesic flow for groups with a contracting element

Résumé

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 dissipative or conservative and ergodic.

Dates et versions

hal-04235294 , version 1 (10-10-2023)

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Rémi Coulon. Ergodicity of the geodesic flow for groups with a contracting element. 2023. ⟨hal-04235294⟩
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