Dynamical zeta functions for Axiom A flows

TL;DR

This paper proves that the Ruelle zeta function for smooth Axiom A flows extends meromorphically across the entire complex plane, advancing understanding of dynamical zeta functions in hyperbolic systems.

Contribution

It establishes the meromorphic continuation of the Ruelle zeta function for Axiom A flows with orientable stable and unstable spaces, building on recent foundational results.

Findings

Meromorphic continuation of Ruelle zeta function proved

Applicable to all smooth Axiom A flows with orientable invariant bundles

Connects hyperbolic set theory with zeta function analysis

Abstract

We show that the Ruelle zeta function of any smooth Axiom A flow with orientable stable/unstable spaces has a meromorphic continuation to the entire complex plane. The proof uses the meromorphic continuation result of [arXiv:1410.5516] together with the work of Conley-Easton and [arXiv:1711.10059] which imply that every basic hyperbolic set can be put into the framework of [arXiv:1410.5516].