{"title":"Rational families converging to a family of exponential maps","authors":"Joanna Furno, J. Hawkins, L. Koss","doi":"10.4171/JFG/70","DOIUrl":null,"url":null,"abstract":"We analyze the dynamics of a sequence of families of non-polynomial rational maps, tfa,du, for a P C ̊ “ Czt0u, d ě 2. For each d, tfa,du is a family of rational maps of degree d of the Riemann sphere parametrized by a P C ̊. For each a P C ̊, as d Ñ 8, fa,d converges uniformly on compact sets to a map fa that is conformally conjugate to a transcendental entire map on C. We study how properties of the families fa,d contribute to our understanding of the dynamical properties of the limiting family of maps. We show all families have a common connectivity locus; moreover the rational maps contain some well-studied examples. Mathematics Subject Classification (2010). 37F10, 37F45, 30D05.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/JFG/70","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/JFG/70","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 3
Abstract
We analyze the dynamics of a sequence of families of non-polynomial rational maps, tfa,du, for a P C ̊ “ Czt0u, d ě 2. For each d, tfa,du is a family of rational maps of degree d of the Riemann sphere parametrized by a P C ̊. For each a P C ̊, as d Ñ 8, fa,d converges uniformly on compact sets to a map fa that is conformally conjugate to a transcendental entire map on C. We study how properties of the families fa,d contribute to our understanding of the dynamical properties of the limiting family of maps. We show all families have a common connectivity locus; moreover the rational maps contain some well-studied examples. Mathematics Subject Classification (2010). 37F10, 37F45, 30D05.
我们分析一个序列的动态的家庭non-polynomial理性的地图,组织,du, P C̊Czt0u dě2。对于每一个d, tfa,du，都是黎曼球的d次有理映射族，由P C _ n参数化。对于每个a P C _，当d Ñ 8时，fa,d在紧集上一致收敛到映射fa，该映射fa与C上的超越全映射共形共轭。我们研究了fa,d族的性质如何有助于我们对极限映射族的动力学性质的理解。我们发现所有的家庭都有一个共同的连接位点;此外，有理图包含了一些研究得很好的例子。数学学科分类(2010)。37f10, 37f45, 30d05。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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