{"title":"A Riemannian metric on hyperbolic components","authors":"Yan Mary He, Hongming Nie","doi":"10.4310/mrl.2023.v30.n3.a6","DOIUrl":null,"url":null,"abstract":"We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree at least $2$ rational maps in one complex variable. Our metric is constructed by considering the measure-theoretic entropy of a rational map with respect to some equilibrium state.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"33 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Research Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/mrl.2023.v30.n3.a6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We introduce a Riemannian metric on certain hyperbolic components in the moduli space of degree at least $2$ rational maps in one complex variable. Our metric is constructed by considering the measure-theoretic entropy of a rational map with respect to some equilibrium state.
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