dc.contributor.author Chung, Nhan-Phu dc.contributor.author Zhang, Guohua dc.date.accessioned 2014-04-25T12:00:00Z dc.date.accessioned 2016-10-05T14:13:57Z dc.date.available 2014-04-25T12:00:00Z dc.date.available 2016-10-05T14:13:57Z dc.date.issued 2014-04-25 dc.identifier.uri http://publications.mfo.de/handle/mfo/1076 dc.description Research in Pairs 2013 en_US dc.description.abstract In this paper, we shall introduce $h$-expansiveness and asymptotical $h$-expansiveness for actions of sofic groups. By the definitions, each h-expansive action of sofic groups is asymptotically $h$-expansive. We show that each expansive action of sofic groups is $h$-expansive, and, for any given asymptotically $h$-expansive action of sofic groups, the entropy function (with respect to measures) is upper semi-continuous and hence the system admits a measure with maximal entropy. Observe that asymptotically $h$-expansive property was firstly introduced and studied by Misiurewicz for $\mathbb{Z}$-actions using the language of tail entropy. And thus in the remaining part of the paper, we shall compare our definitions of weak expansiveness for actions of sofic groups with the definitions given in the same spirit of Misiurewicz's ideas when the group is amenable. It turns out that these two definitions are equivalent in this setting. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2014,05 dc.subject Actions of sofic groups en_US dc.subject Expansive H-expansive en_US dc.subject Asymptotically h-expansive en_US dc.subject Measures with maximal entropy en_US dc.subject Actions of amenable groups en_US dc.title Weak Expansiveness for Actions of Sofic Groups en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2014-05 local.scientificprogram Research in Pairs 2013 local.series.id OWP-2014-05 local.subject.msc 37 local.subject.msc 54
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