Upper semi-continuity of entropy in non-compact settings

Iommi, Godofredo; Todd, Mike; Velozo, Anibal

Abstract

We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous on the set of ergodic measures. Note that the phase space is non-compact. We also discuss the related problem of existence of measures of maximal entropy.

Más información

Título de la Revista: MATHEMATICAL RESEARCH LETTERS
Volumen: 27
Número: 4
Editorial: INTERNATIONAL PRESS
Fecha de publicación: 2020
Página de inicio: 1055
Página final: 1077
URL: https://www.intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0027/0004/a004/