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
Copyright © 2020 International Press of Boston, Inc. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.4310/MRL.2020.v27.n4.a4.
DescriptionFunding: G.I. was partially supported by CONICYT PIA ACT172001 and by Proyecto Fondecyt 1190194.
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