{"title":"Geometric limit of Julia set of a family of rational functions with odd degree","authors":"A. Alves, B. P. Silva e Silva, M. Salarinoghabi","doi":"10.1080/14689367.2021.1993145","DOIUrl":null,"url":null,"abstract":"For a positive odd integer d, we study the connectedness of the Julia set of the one-parameter family of rational maps given by with . Also, when we show that the geometric limit of the Julia set and filled Julia set of the family exists and is the unit circle.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"699 - 713"},"PeriodicalIF":0.5000,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamical Systems-An International Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/14689367.2021.1993145","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
For a positive odd integer d, we study the connectedness of the Julia set of the one-parameter family of rational maps given by with . Also, when we show that the geometric limit of the Julia set and filled Julia set of the family exists and is the unit circle.
期刊介绍：
Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal:
•Differential equations
•Bifurcation theory
•Hamiltonian and Lagrangian dynamics
•Hyperbolic dynamics
•Ergodic theory
•Topological and smooth dynamics
•Random dynamical systems
•Applications in technology, engineering and natural and life sciences
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