{"title":"An upper bound for the box dimension of the hyperbolic dynamics via unstable topological pressure","authors":"Congcong Qu","doi":"10.1016/j.na.2024.113560","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we utilize the sub-additive unstable topological pressure to give an upper bound for the upper box dimension of the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> hyperbolic set on local unstable manifold. As a by-product, we give a new expression of the topological pressure on symbolic spaces. This work is inspired by Barreira (1996), Feng and Simon (2023) and Zhang et al. (2022).</p></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"245 ","pages":"Article 113560"},"PeriodicalIF":1.3000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24000798","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/5/8 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we utilize the sub-additive unstable topological pressure to give an upper bound for the upper box dimension of the hyperbolic set on local unstable manifold. As a by-product, we give a new expression of the topological pressure on symbolic spaces. This work is inspired by Barreira (1996), Feng and Simon (2023) and Zhang et al. (2022).
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