Olivier Glorieux, Daniel Monclair, Nicolas Tholozan
{"title":"Hausdorff dimension of limit sets for projective Anosov representations","authors":"Olivier Glorieux, Daniel Monclair, Nicolas Tholozan","doi":"10.5802/jep.241","DOIUrl":null,"url":null,"abstract":"We study the relation between critical exponents and Hausdorff dimensions of limit sets for projective Anosov representations. We prove that the Hausdorff dimension of the symmetric limit set in $\\mathbf{P}(\\mathbb{R}^{n}) \\times \\mathbf{P}({\\mathbb{R}^{n}}^*)$ is bounded between two critical exponents associated respectively to a highest weight and a simple root.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"129 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de l’École polytechnique — Mathématiques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/jep.241","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 10
Abstract
We study the relation between critical exponents and Hausdorff dimensions of limit sets for projective Anosov representations. We prove that the Hausdorff dimension of the symmetric limit set in $\mathbf{P}(\mathbb{R}^{n}) \times \mathbf{P}({\mathbb{R}^{n}}^*)$ is bounded between two critical exponents associated respectively to a highest weight and a simple root.