Upper semi-continuity of entropy in non-compact settings
Dynamical Systems
2021-08-16 v2
Abstract
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous at ergodic measures. Note that the phase space is non-compact. Applications to systems that can be coded by these shifts, such as positive entropy diffeomorphisms on compact manifolds, are given. We also discuss the related problem of existence of measures of maximal entropy.
Cite
@article{arxiv.1809.10022,
title = {Upper semi-continuity of entropy in non-compact settings},
author = {Godofredo Iommi and Mike Todd and Aníbal Velozo},
journal= {arXiv preprint arXiv:1809.10022},
year = {2021}
}
Comments
Some errors in applications corrected