{"title":"随机线性共环的动态性质","authors":"Manseob Lee, Jumi Oh","doi":"10.1142/s179355712350208x","DOIUrl":null,"url":null,"abstract":"In this paper, we extend the expansivity, pseudo trajectory tracing property and hyperbolicity of linear dynamical systems for the random view point. We show that to a random linear cocycle [Formula: see text] it is expansive if and only if it has the generalized pseudo trajectory tracing property. Moreover, we show that [Formula: see text] is topologically stable if and only if it is structurally stable.","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamic properties of random linear cocycles\",\"authors\":\"Manseob Lee, Jumi Oh\",\"doi\":\"10.1142/s179355712350208x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we extend the expansivity, pseudo trajectory tracing property and hyperbolicity of linear dynamical systems for the random view point. We show that to a random linear cocycle [Formula: see text] it is expansive if and only if it has the generalized pseudo trajectory tracing property. Moreover, we show that [Formula: see text] is topologically stable if and only if it is structurally stable.\",\"PeriodicalId\":45737,\"journal\":{\"name\":\"Asian-European Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-09-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Asian-European Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s179355712350208x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian-European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s179355712350208x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we extend the expansivity, pseudo trajectory tracing property and hyperbolicity of linear dynamical systems for the random view point. We show that to a random linear cocycle [Formula: see text] it is expansive if and only if it has the generalized pseudo trajectory tracing property. Moreover, we show that [Formula: see text] is topologically stable if and only if it is structurally stable.
期刊介绍：
Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.
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