November 9, 2025Open Access

Uniqueness of the measure of maximal entropy for geodesic flows on coarse hyperbolic manifolds without conjugate points

Key Points

A unique measure of maximal entropy exists for geodesic flows on certain hyperbolic manifolds.
The study focuses on closed Riemannian manifolds without conjugate points, finding significant properties of geodesic rays.
The methodology explores conditions under which the geodesic flows possess this unique measure, broadening prior research findings.
These results may advance understanding of the dynamics of geodesic flows in Riemannian geometry and its implications in broader mathematical contexts.

Abstract

In this article we study geodesic flows on closed Riemannian manifolds without conjugate points and divergence property of geodesic rays. If the fundamental group is Gromov hyperbolic and residually finite we prove, under appropriate assumptions on the expansive set, that the geodesic flow has a unique measure of maximal entropy. This generalizes corresponding results of Climenhaga, Knieper and War proved under the stronger assumption of the existence of a background metric of negative sectional curvature.

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Authors

Gerhard Knieper

Ruhr University Bochum

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Uniqueness of the measure of maximal entropy for geodesic flows on coarse hyperbolic manifolds without conjugate points

Key Points

Abstract

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Authors

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Citation Network

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