{"title":"广义马蹄图的绝对连续不变度量","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":"{\"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}","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}
Absolutely Continuous Invariant Measure for Generalized Horseshoe Maps
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.