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Closed orbits in homology classes for Anosov flows

Published online by Cambridge University Press:  19 September 2008

Richard Sharp
Richard Sharp*
Affiliation:
Institut des Hautes Etudes Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, France
*
†School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK.
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Abstract

We consider transitive Anosov flows φ: M → M and give necessary and sufficient conditions for every homology class in H1(M,ℤ) to contain a closed φ-orbit. Under these conditions, we derive an asymptotic formula for the number of closed φ-orbits in a fixed homology class, generalizing a result of Katsuda and Sunada.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 2 , June 1993 , pp. 387 - 408
Copyright
Copyright © Cambridge University Press 1993

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