{"title":"环形迭代函数系统的旋转熵","authors":"Fatemeh Rezaei, M. F. Nia","doi":"10.1080/1726037X.2021.2009199","DOIUrl":null,"url":null,"abstract":"Abstract In this article, we consider an iterated functions system (IFS) whose functions are homeomorphisms on an annulus. We define rotational spanning and separating sets for the IFS and then provide two definitions for the rotational entropy of the IFS. We show that in the IFSs, the rotational entropy is a topological invariant. We prove that the rotational entropy of an annular IFS is equal to the rotational entropy on its non-wandering set for sequences of functions with a specific condition.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"19 1","pages":"189 - 202"},"PeriodicalIF":0.4000,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rotational Entropy of an Annular Iterated Functions System\",\"authors\":\"Fatemeh Rezaei, M. F. Nia\",\"doi\":\"10.1080/1726037X.2021.2009199\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this article, we consider an iterated functions system (IFS) whose functions are homeomorphisms on an annulus. We define rotational spanning and separating sets for the IFS and then provide two definitions for the rotational entropy of the IFS. We show that in the IFSs, the rotational entropy is a topological invariant. We prove that the rotational entropy of an annular IFS is equal to the rotational entropy on its non-wandering set for sequences of functions with a specific condition.\",\"PeriodicalId\":42788,\"journal\":{\"name\":\"Journal of Dynamical Systems and Geometric Theories\",\"volume\":\"19 1\",\"pages\":\"189 - 202\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamical Systems and Geometric Theories\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/1726037X.2021.2009199\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamical Systems and Geometric Theories","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/1726037X.2021.2009199","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Rotational Entropy of an Annular Iterated Functions System
Abstract In this article, we consider an iterated functions system (IFS) whose functions are homeomorphisms on an annulus. We define rotational spanning and separating sets for the IFS and then provide two definitions for the rotational entropy of the IFS. We show that in the IFSs, the rotational entropy is a topological invariant. We prove that the rotational entropy of an annular IFS is equal to the rotational entropy on its non-wandering set for sequences of functions with a specific condition.
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