{"title":"正弱测度扩张可微映射","authors":"Jiweon Ahn, Manseob Lee","doi":"10.4134/BKMS.B181190","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce the new general concept of usual expansiveness which is called “positively weak measure expansiveness” and study the basic properties of positively weak measure expansive C1differentiable maps on a compact smooth manifold M . And we prove that the following theorems. (1) Let PWE be the set of all positively weak measure expansive differentiable maps of M . Denote by int(PWE) is a C1-interior of PWE. f ∈ int(PWE) if and only if f is expanding. (2) For C1-generic f ∈ C1(M), f is positively weak measure-expansive if and only if f is expanding.","PeriodicalId":55301,"journal":{"name":"Bulletin of the Korean Mathematical Society","volume":"57 1","pages":"569-581"},"PeriodicalIF":0.6000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"POSITIVELY WEAK MEASURE EXPANSIVE DIFFERENTIABLE MAPS\",\"authors\":\"Jiweon Ahn, Manseob Lee\",\"doi\":\"10.4134/BKMS.B181190\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce the new general concept of usual expansiveness which is called “positively weak measure expansiveness” and study the basic properties of positively weak measure expansive C1differentiable maps on a compact smooth manifold M . And we prove that the following theorems. (1) Let PWE be the set of all positively weak measure expansive differentiable maps of M . Denote by int(PWE) is a C1-interior of PWE. f ∈ int(PWE) if and only if f is expanding. (2) For C1-generic f ∈ C1(M), f is positively weak measure-expansive if and only if f is expanding.\",\"PeriodicalId\":55301,\"journal\":{\"name\":\"Bulletin of the Korean Mathematical Society\",\"volume\":\"57 1\",\"pages\":\"569-581\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Korean Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4134/BKMS.B181190\",\"RegionNum\":4,\"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":"Bulletin of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/BKMS.B181190","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we introduce the new general concept of usual expansiveness which is called “positively weak measure expansiveness” and study the basic properties of positively weak measure expansive C1differentiable maps on a compact smooth manifold M . And we prove that the following theorems. (1) Let PWE be the set of all positively weak measure expansive differentiable maps of M . Denote by int(PWE) is a C1-interior of PWE. f ∈ int(PWE) if and only if f is expanding. (2) For C1-generic f ∈ C1(M), f is positively weak measure-expansive if and only if f is expanding.
期刊介绍：
This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).
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