{"title":"Bounded hyperbolic components of bicritical rational maps","authors":"Hongming Nie, K. Pilgrim","doi":"10.3934/jmd.2022016","DOIUrl":null,"url":null,"abstract":"We prove that the hyperbolic components of bicritical rational maps having two distinct attracting cycles each of period at least two are bounded in the moduli space of bicritical rational maps. Our arguments rely on arithmetic methods.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Modern Dynamics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/jmd.2022016","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 6
Abstract
We prove that the hyperbolic components of bicritical rational maps having two distinct attracting cycles each of period at least two are bounded in the moduli space of bicritical rational maps. Our arguments rely on arithmetic methods.
期刊介绍：
The Journal of Modern Dynamics (JMD) is dedicated to publishing research articles in active and promising areas in the theory of dynamical systems with particular emphasis on the mutual interaction between dynamics and other major areas of mathematical research, including:
Number theory
Symplectic geometry
Differential geometry
Rigidity
Quantum chaos
Teichmüller theory
Geometric group theory
Harmonic analysis on manifolds.
The journal is published by the American Institute of Mathematical Sciences (AIMS) with the support of the Anatole Katok Center for Dynamical Systems and Geometry at the Pennsylvania State University.
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