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Approximate solutions of cohomological equations associated with some Anosov flows

Published online by Cambridge University Press:  19 September 2008

Svetlana Katok
Svetlana Katok
Affiliation:
Department of Mathematics, University of California, Santa Cruz, Santa Cruz, CA 95064, USA
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Abstract

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The Livshitz theorem reported in 1971 asserts that any C1 function having zero integrals over all periodic orbits of a topologically transitive Anosov flow is a derivative of another C1 function in the direction of the flow. Similar results for functions of higher differentiability have also appeared since. In this paper we prove a ‘finite version’ of the Livshitz theorem for a certain class of Anosov flows on 3-dimensional manifolds which include geodesic flows on negatively curved surfaces as a special case.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 2 , June 1990 , pp. 367 - 379
Copyright
Copyright © Cambridge University Press 1990

References

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