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- W2036129981 abstract "Let Γ be a nonelementary Kleinian group acting on a Cartan-Hadamard manifold $tilde{X}$; denote by Λ(Γ) the nonwandering set of the geodesic flow (φt) acting on the unit tangent bundle T1($tilde{X}$/Γ). When Γ is convex cocompact (i.e., Λ(Γ) is compact), the restriction of (φt) to Λ(Γ) is an Axiom A flow: therefore, by a theorem of Bowen and Ruelle, there exists a unique invariant measure on Λ(Γ) which has maximal entropy. In this paper, we study the case of an arbitrary Kleinian group Γ. We show that there exists a measure of maximal entropy for the restriction of(φt) to Λ(Γ) if and only if the Patterson-Sullivan measure is finite; furthermore when this measure is finite, it is the unique measure of maximal entropy. By a theorem of Handel and Kitchens, the supremum of the measure-theoretic entropies equals the infimum of the entropies of the distances d on Λ(X); when Γ is geometrically finite, we show that this infimum is achieved by the Riemannian distance d on Λ(X)." @default.
- W2036129981 created "2016-06-24" @default.
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- W2036129981 date "2004-10-01" @default.
- W2036129981 modified "2023-09-27" @default.
- W2036129981 title "Principe variationnel et groupes Kleiniens" @default.
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- W2036129981 doi "https://doi.org/10.1215/s0012-7094-04-12512-6" @default.
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