Upper semi-continuity of entropy in non-compact settings

Godofredo Iommi, Michael John Todd, Aníbal Velozo

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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.
Original languageEnglish
Pages (from-to)1055-1077
JournalMathematical Research Letters
Issue number4
Publication statusPublished - 14 Dec 2020


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