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

Abstract

For an Axiom A flow restricted to a basic set we extend the zeta function to an open set containing W(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.