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Bowen's equidistribution theory and the Dirichlet density theorem

Published online by Cambridge University Press:  19 September 2008

William Parry
William Parry
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, England
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Abstract

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Let φ be an Axiom A flow restricted to a basic set, let g be a C∞ function and let , where λg(τ) is the g length of the closest orbit τ, λ(τ) is the period of τ and h is the topological entropy of φ. We obtain an asymptotic formula for πg which includes the ‘prime number’ theorem for closed orbits. This result generalizes Bowen's theorem on the equidistribution of closed orbits. After establishing an analytic extension result for certain zeta functions the proofs proceed by orthodox number theoretical techniques.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 1 , March 1984 , pp. 117 - 134
Copyright
Copyright © Cambridge University Press 1984

References

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