Ruelle's inequality in negative curvature
Dynamical Systems
2018-01-17 v3
Abstract
In this paper we study different notions of entropy for measure-preserving dynamical systems defined on noncompact spaces. We see that some classical results for compact spaces remain partially valid in this setting. We define a new kind of entropy for dynamical systems defined on noncompact Riemannian manifolds, which satisfies similar properties to the classical ones. As an application, we prove Ruelle's inequality and Pesin's entropy formula for the geodesic flow in manifolds with pinched negative sectional curvature.
Keywords
Cite
@article{arxiv.1601.02843,
title = {Ruelle's inequality in negative curvature},
author = {Felipe Riquelme},
journal= {arXiv preprint arXiv:1601.02843},
year = {2018}
}
Comments
Final version, focused only on the case of the geodesic flow in negative curvature