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Pairs of periodic orbits with fixed homology difference

Part of: Dynamical systems with hyperbolic behavior Smooth dynamical systems: general theory

Published online by Cambridge University Press:  12 August 2010

Morten S. Risager  and
Richard Sharp
Morten S. Risager
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark ([email protected])
Richard Sharp
Affiliation:
School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK ([email protected])
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Abstract

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We obtain an asymptotic formula for the number of pairs of closed orbits of a weak-mixing transitive Anosov flow whose homology classes have a fixed difference.

Keywords

Anosov flowperiodic orbithomologyclosed geodesicthermodynamic formalism

MSC classification

Secondary: 37C27: Periodic orbits of vector fields and flows 37C30: Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 37D35: Thermodynamic formalism, variational principles, equilibrium states 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 3 , October 2010 , pp. 799 - 808
Copyright
Copyright © Edinburgh Mathematical Society 2010

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