{"title":"无限维瑟斯顿理论与先验动力学I:无限腿蜘蛛","authors":"K. Bogdanov","doi":"10.4064/fm82-11-2022","DOIUrl":null,"url":null,"abstract":"We develop techniques that lay out a basis for generalizations of the famous Thurston's Topological Characterization of Rational Functions for an infinite set of marked points and branched coverings of infinite degree. Analogously to the classical theorem we consider the Thurston's $\\sigma$-map acting on a Teichm\\\"uller space which is this time infinite-dimensional -- and this leads to a completely different theory comparing to the classical setting. We demonstrate our techniques by giving an alternative proof of the result by Markus F\\\"orster about the classification of exponential functions with the escaping singular value.","PeriodicalId":55138,"journal":{"name":"Fundamenta Mathematicae","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Infinite-dimensional Thurston theory and transcendental dynamics I: infinite-legged spiders\",\"authors\":\"K. Bogdanov\",\"doi\":\"10.4064/fm82-11-2022\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We develop techniques that lay out a basis for generalizations of the famous Thurston's Topological Characterization of Rational Functions for an infinite set of marked points and branched coverings of infinite degree. Analogously to the classical theorem we consider the Thurston's $\\\\sigma$-map acting on a Teichm\\\\\\\"uller space which is this time infinite-dimensional -- and this leads to a completely different theory comparing to the classical setting. We demonstrate our techniques by giving an alternative proof of the result by Markus F\\\\\\\"orster about the classification of exponential functions with the escaping singular value.\",\"PeriodicalId\":55138,\"journal\":{\"name\":\"Fundamenta Mathematicae\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-01-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamenta Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/fm82-11-2022\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/fm82-11-2022","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Infinite-dimensional Thurston theory and transcendental dynamics I: infinite-legged spiders
We develop techniques that lay out a basis for generalizations of the famous Thurston's Topological Characterization of Rational Functions for an infinite set of marked points and branched coverings of infinite degree. Analogously to the classical theorem we consider the Thurston's $\sigma$-map acting on a Teichm\"uller space which is this time infinite-dimensional -- and this leads to a completely different theory comparing to the classical setting. We demonstrate our techniques by giving an alternative proof of the result by Markus F\"orster about the classification of exponential functions with the escaping singular value.
期刊介绍:
FUNDAMENTA MATHEMATICAE concentrates on papers devoted to
Set Theory,
Mathematical Logic and Foundations of Mathematics,
Topology and its Interactions with Algebra,
Dynamical Systems.