Ergodic Theory and Dynamical Systems

Research Article

Meromorphic extension of the zeta function for Axiom A flows

Nicolai T. A. Haydna1

a1 Department of Mathematics, University of Toronto, Toronto M5S 1A1, Canada

Abstract

We prove the meromorphicity of the zeta function on shifts of finite type for Hölder continuous functions assuming that the essential spectrum of the associated Ruelle operator is contained in the open unit disc. This result allows to extend the region of meromorphicity of the zeta function for Axiom A flows by a strip whose width is determined by the contraction rate of the flow.

(Received April 22 1988)

(Revised October 10 1988)