{"title":"Dimensions of harmonic measures on non-autonomous Cantor sets","authors":"Athanasios Batakis, Guillaume Havard","doi":"arxiv-2409.08019","DOIUrl":null,"url":null,"abstract":"We consider Non Autonomous Conformal Iterative Function Systems (NACIFS) and\ntheir limit set. Our main concern is harmonic measure and its dimensions :\nHausdorff and Packing. We prove that this two dimensions are continuous under\nperturbations and that they verify Bowen's and Manning's type formulas. In\norder to do so we prove general results about measures, and more generally\nabout positive functionals, defined on a symbolic space, developing tools from\nthermodynamical formalism in a non-autonomous setting.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08019","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 consider Non Autonomous Conformal Iterative Function Systems (NACIFS) and
their limit set. Our main concern is harmonic measure and its dimensions :
Hausdorff and Packing. We prove that this two dimensions are continuous under
perturbations and that they verify Bowen's and Manning's type formulas. In
order to do so we prove general results about measures, and more generally
about positive functionals, defined on a symbolic space, developing tools from
thermodynamical formalism in a non-autonomous setting.