{"title":"DYNAMICS OF THE FAMILY tan z2","authors":"Santanu Nandi","doi":"10.17654/DS032020067","DOIUrl":null,"url":null,"abstract":"This article discusses some topological properties of the dynamical plane ($z$-plane) of the holomorphic family of meromorphic maps $\\lambda \\tan z^2$ for $ \\lambda \\in \\mathbb C^*$. In the dynamical plane, I prove that there is no Herman ring and the Julia set is a Cantor set for the maps when the parameter is in the hyperbolic component containing the origin. Julia set is connected for the maps when the parameters are in other hyperbolic components in the parameter plane.","PeriodicalId":330387,"journal":{"name":"Far East Journal of Dynamical Systems","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Far East Journal of Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17654/DS032020067","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
This article discusses some topological properties of the dynamical plane ($z$-plane) of the holomorphic family of meromorphic maps $\lambda \tan z^2$ for $ \lambda \in \mathbb C^*$. In the dynamical plane, I prove that there is no Herman ring and the Julia set is a Cantor set for the maps when the parameter is in the hyperbolic component containing the origin. Julia set is connected for the maps when the parameters are in other hyperbolic components in the parameter plane.
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