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Closed orbits in homology classes for Anosov flows

  • Richard Sharp (a1)
Abstract
Abstract

We consider transitive Anosov flows φ: MM 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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School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK.
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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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