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Journal Article

An Analogue of the Prime Number Theorem for Closed Orbits of Axiom a Flows

William Parry and Mark Pollicott
Annals of Mathematics
Second Series, Vol. 118, No. 3 (Nov., 1983), pp. 573-591
Published by: Annals of Mathematics
DOI: 10.2307/2006982
Stable URL: http://www.jstor.org/stable/2006982
Page Count: 19
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An Analogue of the Prime Number Theorem for Closed Orbits of Axiom a Flows
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Abstract

For an Axiom A flow restricted to a basic set we extend the zeta function to an open set containing R(s) ≥ h where h is the topological entropy. This enables us to give an asymptotic formula for the number of closed orbits by adapting the Wiener-Ikehara proof of the prime number theorem.

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