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dc.contributor.authorIommi, Godofredo
dc.contributor.authorTodd, Mike
dc.contributor.authorVelozo, Aníbal
dc.identifier.citationIommi , G , Todd , M & Velozo , A 2022 , ' Escape of entropy for countable Markov shifts ' , Advances in Mathematics , vol. 405 , 108507 .
dc.identifier.otherPURE: 260728051
dc.identifier.otherPURE UUID: a332d0dc-9f2f-4f0e-ab59-c808b7f083e9
dc.identifier.otherORCID: /0000-0002-0042-0713/work/114977452
dc.identifier.otherScopus: 85131758933
dc.descriptionFunding: GI was partially supported by CONICYT PIA ACT172001 and by Proyecto Fondecyt 1190194. AV was supported by Proyecto Fondecyt Iniciación 11220409.en
dc.description.abstractIn this paper we study ergodic theory of countable Markov shifts. These are dynamical systems defined over non-compact spaces. Our main result relates the escape of mass, the measure theoretic entropy, and the entropy at infinity of the system. This relation has several consequences. For example we obtain that the entropy map is upper semi-continuous and that the ergodic measures form an entropy dense subset. Our results also provide new proofs of results describing the existence and stability of the measure of maximal entropy. We relate the entropy at infinity with the Hausdorff dimension of the set of recurrent points that escape on average. Of independent interest, we prove a version of Katok’s entropy formula in this non-compact setting.
dc.relation.ispartofAdvances in Mathematicsen
dc.rightsCopyright © 2022 Elsevier 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
dc.subjectMarkov shiftsen
dc.subjectEscape of massen
dc.subjectQA Mathematicsen
dc.titleEscape of entropy for countable Markov shiftsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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