On Ruelle's Lemma and Ruelle Zeta Functions
Dynamical Systems
2010-10-25 v1
Abstract
In this article we prove an important inequality regarding the Ruelle operator in hyperbolic flows. This was already proven briefly by Mark Pollicott and Richard Sharp in a low dimensional case, but we present a clearer proof of the inequality, filling in gaps and explaining the ideas in more detail, and extend the inequality to higher dimensional flows. This inequality is necessary to prove a proposition about the analyticity of Ruelle zeta functions.
Keywords
Cite
@article{arxiv.1010.4607,
title = {On Ruelle's Lemma and Ruelle Zeta Functions},
author = {Paul Wright},
journal= {arXiv preprint arXiv:1010.4607},
year = {2010}
}
Comments
This article represents the main result of the author's honours dissertation at the University of Western Australia, supervised by Luchezar Stoyanov