Upper semi-continuity of entropy in non-compact settings
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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.
Iommi , G , Todd , M J & Velozo , A 2020 , ' Upper semi-continuity of entropy in non-compact settings ' , Mathematical Research Letters , vol. 27 , no. 4 , pp. 1055-1077 . https://doi.org/10.4310/MRL.2020.v27.n4.a4
Mathematical Research Letters
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DescriptionFunding: G.I. was partially supported by CONICYT PIA ACT172001 and by Proyecto Fondecyt 1190194.
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