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Time-preserving conjugacies of geodesic flows

Published online by Cambridge University Press:  19 September 2008

Ursula Hamenstädt
Ursula Hamenstädt
Affiliation:
Mathematisches Institut der Universität Bonn, Beringstraβe 1, 5300 Bonn, Germany
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Abstract

In this note we study Borel-probability measures on the unit tangent bundle ofa compact negatively curved manifold M that are invariant under the geodesic flow. We interpret the entropy of such a measure as a Hausdorff dimension with respect to a natural family of distances on the ideal boundary of the universal covering of M. This in term yields necessary and sufficient conditions for the existence of time preserving conjugacies of geodesic flows.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 1 , March 1992 , pp. 67 - 74
Copyright
Copyright © Cambridge University Press 1992

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