Anosov Flows and Dynamical Zeta Functions (Errata)

TL;DR

This paper provides an erratum to a previous work on Anosov flows, correcting a mistake related to the spectral gap for contact Anosov flows but confirming the meromorphic nature of the Ruelle zeta function.

Contribution

It corrects a specific error in the spectral gap proof for contact Anosov flows while affirming the meromorphic property of the Ruelle zeta function.

Findings

Corrected the spectral gap proof for contact Anosov flows.

Confirmed the Ruelle zeta function is meromorphic.

Clarified the scope of previous results.

Abstract

This errata fixes a mistake in the part of Giulietti, P.; Liverani, C.; Pollicott, M. Anosov flows and dynamical zeta functions. Ann. of Math. (2) {\bf 178} (2013), no. 2, 687--773, which proves a spectral gap for contact Anosov flows with respect to the measure of maximal entropy (Section 7). However, the first part of the paper, in which it is proved that the Ruelle zeta function is meromorphic, is unaffected.