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Distribution of closed geodesics with a preassigned homology class in a negatively curved manifold

Published online by Cambridge University Press:  22 January 2016

Toshiaki Adachi
Toshiaki Adachi*
Affiliation:
Department of Mathematics, Nagoya University, Chikusa-ku Nagoya, 464Japan
*
Department of Mathematics, College of General Education, Kumamoto University, Kumamoto, 860Japan
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Let M be a compact Riemannian manifold whose geodesic flow φi : UM→UM on the unit tangent bundle is of Anosov type. In this paper we count the number of φi-closed orbits and study the distribution of prime closed geodesies in a given homology class in H1(M, Z). Here a prime closed geodesic means an (oriented) image of a φi-closed orbit by the projection p : UM → M.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 110 , June 1988 , pp. 1 - 14
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

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