Upper semi-continuity of entropy in non-compact settings

Godofredo Iommi; Michael John Todd; Aníbal Velozo

doi:10.4310/MRL.2020.v27.n4.a4

Upper semi-continuity of entropy in non-compact settings

Godofredo Iommi, Michael John Todd, Aníbal Velozo

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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.

Original language	English
Pages (from-to)	1055-1077
Journal	Mathematical Research Letters
Volume	27
Issue number	4
DOIs	https://doi.org/10.4310/MRL.2020.v27.n4.a4
Publication status	Published - 14 Dec 2020

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10.4310/MRL.2020.v27.n4.a4

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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.
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title = "Upper semi-continuity of entropy in non-compact settings",

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.",

author = "Godofredo Iommi and Todd, {Michael John} and An{\'i}bal Velozo",

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T1 - Upper semi-continuity of entropy in non-compact settings

AU - Iommi, Godofredo

AU - Todd, Michael John

AU - Velozo, Aníbal

N1 - Funding: G.I. was partially supported by CONICYT PIA ACT172001 and by Proyecto Fondecyt 1190194.

PY - 2020/12/14

Y1 - 2020/12/14

N2 - 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.

AB - 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.

U2 - 10.4310/MRL.2020.v27.n4.a4

DO - 10.4310/MRL.2020.v27.n4.a4

M3 - Article

SN - 1073-2780

VL - 27

SP - 1055

EP - 1077

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 4

ER -

Upper semi-continuity of entropy in non-compact settings

Abstract

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