Rigidity of measures—The high entropy case and non-commuting foliations
Identifieur interne : 001168 ( Istex/Corpus ); précédent : 001167; suivant : 001169Rigidity of measures—The high entropy case and non-commuting foliations
Auteurs : Manfred Einsiedler ; Anatole KatokSource :
- Israel Journal of Mathematics [ 0021-2172 ] ; 2005-12-01.
Abstract
Abstract: We consider invariant measures for partially hyperbolic, semisimple, higher rank actions on homogeneous spaces defined by products of real andp-adic Lie groups. In this paper we generalize our earlier work to establish measure rigidity in the high entropy case in that setting. We avoid any additional ergodicity-type assumptions but rely on, and extend the theory of conditional measures.
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DOI: 10.1007/BF02775436
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In this paper we generalize our earlier work to establish measure rigidity in the high entropy case in that setting. We avoid any additional ergodicity-type assumptions but rely on, and extend the theory of conditional measures.</Para></Abstract><ArticleNote Type="Dedication"><SimplePara>To Hillel Furstenberg with friendship and admiration</SimplePara></ArticleNote><ArticleNote Type="Misc"><SimplePara>Manfred Einsiedler is partially supported by the NSF Grant DMS 0400587.</SimplePara></ArticleNote><ArticleNote Type="Misc"><SimplePara>Anatole Katok is partially supported by the NSF Grant DMS 0071339.</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Rigidity of measures—The high entropy case and non-commuting foliations</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Rigidity of measures—The high entropy case and non-commuting foliations</title></titleInfo><name type="personal" displayLabel="corresp"><namePart type="given">Manfred</namePart><namePart type="family">Einsiedler</namePart><affiliation>Department of Mathematics, Box 354350, University of Washington, 98195, Seattle, WA, USA</affiliation><affiliation>E-mail: einsiedl@math.washington.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Anatole</namePart><namePart type="family">Katok</namePart><affiliation>Department of Mathematics, Penn State University, 16802, State College, PA, USA</affiliation><affiliation>E-mail: kotok_a@math.psu.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">New York</placeTerm></place><dateCreated encoding="w3cdtf">2004-03-07</dateCreated><dateIssued encoding="w3cdtf">2005-12-01</dateIssued><dateIssued encoding="w3cdtf">2005</dateIssued><copyrightDate encoding="w3cdtf">2005</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: We consider invariant measures for partially hyperbolic, semisimple, higher rank actions on homogeneous spaces defined by products of real andp-adic Lie groups. 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