{"title":"在一维空间中映射出无限熵","authors":"P. Hazard","doi":"10.4310/arkiv.2020.v58.n1.a7","DOIUrl":null,"url":null,"abstract":"We give examples of endomorphisms in dimension one with infinite topological entropy which are $\\alpha$-H\\\"older and $(1,p)$-Sobolev for all $0\\leq\\alpha<1$ and $1\\leq p<\\infty$. This is constructed within a family of endomorphisms with infinite topological entropy and which traverse all $\\alpha$-H\\\"older and $(1,p)$-Sobolev classes. Finally, we also give examples of endomorphisms, also in dimension one, which lie in the big and little Zygmund classes, answering a question of M. Benedicks.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2017-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Maps in dimension one with infinite entropy\",\"authors\":\"P. Hazard\",\"doi\":\"10.4310/arkiv.2020.v58.n1.a7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give examples of endomorphisms in dimension one with infinite topological entropy which are $\\\\alpha$-H\\\\\\\"older and $(1,p)$-Sobolev for all $0\\\\leq\\\\alpha<1$ and $1\\\\leq p<\\\\infty$. This is constructed within a family of endomorphisms with infinite topological entropy and which traverse all $\\\\alpha$-H\\\\\\\"older and $(1,p)$-Sobolev classes. Finally, we also give examples of endomorphisms, also in dimension one, which lie in the big and little Zygmund classes, answering a question of M. Benedicks.\",\"PeriodicalId\":55569,\"journal\":{\"name\":\"Arkiv for Matematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2017-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arkiv for Matematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/arkiv.2020.v58.n1.a7\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arkiv for Matematik","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/arkiv.2020.v58.n1.a7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We give examples of endomorphisms in dimension one with infinite topological entropy which are $\alpha$-H\"older and $(1,p)$-Sobolev for all $0\leq\alpha<1$ and $1\leq p<\infty$. This is constructed within a family of endomorphisms with infinite topological entropy and which traverse all $\alpha$-H\"older and $(1,p)$-Sobolev classes. Finally, we also give examples of endomorphisms, also in dimension one, which lie in the big and little Zygmund classes, answering a question of M. Benedicks.