{"title":"Multifractal analysis of homological growth rates for hyperbolic surfaces","authors":"JOHANNES JAERISCH, HIROKI TAKAHASI","doi":"10.1017/etds.2024.62","DOIUrl":null,"url":null,"abstract":"We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level sets of prescribed growth rates in terms of a generalized Poincaré exponent of the Fuchsian group. We employ symbolic dynamics developed by Bowen and Series, ergodic theory and thermodynamic formalism to prove the analyticity of the dimension spectrum.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/etds.2024.62","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level sets of prescribed growth rates in terms of a generalized Poincaré exponent of the Fuchsian group. We employ symbolic dynamics developed by Bowen and Series, ergodic theory and thermodynamic formalism to prove the analyticity of the dimension spectrum.