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Invariant measures under geodesic flow

Fanai, H. R ; Sharif University of Technology | 2007

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  1. Type of Document: Article
  2. Publisher: 2007
  3. Abstract:
  4. For a compact Riemannian manifold with negative curvature, the Liouville measure, the Bowen-Margulis measure and the Harmonic measure are three natural invariant measures under the geodesic flow. We show that if any two of the above three measure classes coincide then the space is locally symmetric, provided the function with respect to which the equilibrium state is the Harmonic measure, depends only on the foot points. © 2007 University of Houston
  5. Keywords:
  6. Geodesic flow ; Invariant measures
  7. Source: Houston Journal of Mathematics ; Volume 33, Issue 1 , 2007 , Pages 163-167 ; 03621588 (ISSN)
  8. URL: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.431.2001&rep=rep1&type=pdf