{"title":"Absolutely Continuous Invariant Measure for Generalized Horseshoe Maps","authors":"Abbas Fakhari, Maryam Khalaj, Mohammad Soufi","doi":"10.1007/s00574-024-00402-x","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we study the Sinai–Ruelle–Bowen (SRB) measures of generalized horseshoe maps. We prove that under the conditions of transversality and fatness, the SRB measure is indeed absolutely continuous with respect to the Lebesgue measure.</p>","PeriodicalId":501417,"journal":{"name":"Bulletin of the Brazilian Mathematical Society, New Series","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Brazilian Mathematical Society, New Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00574-024-00402-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we study the Sinai–Ruelle–Bowen (SRB) measures of generalized horseshoe maps. We prove that under the conditions of transversality and fatness, the SRB measure is indeed absolutely continuous with respect to the Lebesgue measure.
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