{"title":"Horocycle averages on closed manifolds and transfer operators","authors":"Alexander Adam, V. Baladi","doi":"10.2140/tunis.2022.4.387","DOIUrl":null,"url":null,"abstract":"We study semigroups of weighted transfer operators for Anosov flows of regularity C^r, r>1, on compact manifolds without boundary. We construct an anisotropic Banach space on which the resolvent of the generator is quasi-compact and where the upper bound on the essential spectral radius depends continuously on the regularity. We apply this result to the ergodic average of the horocycle flow for C^3 contact Anosov flows in dimension three.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tunisian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/tunis.2022.4.387","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 21
Abstract
We study semigroups of weighted transfer operators for Anosov flows of regularity C^r, r>1, on compact manifolds without boundary. We construct an anisotropic Banach space on which the resolvent of the generator is quasi-compact and where the upper bound on the essential spectral radius depends continuously on the regularity. We apply this result to the ergodic average of the horocycle flow for C^3 contact Anosov flows in dimension three.