{"title":"有限维弱拓扑空间中线性微分方程的Li-Yorke混沌","authors":"Xu Zhang, Nan Jiang, Qigui Yang, Guanrong Chen","doi":"10.1063/5.0163463","DOIUrl":null,"url":null,"abstract":"Li–Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology is introduced. Based on this topology on the Euclidean space, a flow generated from a linear differential equation is proved to be Li–Yorke chaotic under certain conditions, which is in sharp contract to the well-known fact that linear differential equations cannot be chaotic in a finite-dimensional space with a strong topology.","PeriodicalId":340975,"journal":{"name":"Chaos: An Interdisciplinary Journal of Nonlinear Science","volume":"180 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Li–Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology\",\"authors\":\"Xu Zhang, Nan Jiang, Qigui Yang, Guanrong Chen\",\"doi\":\"10.1063/5.0163463\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Li–Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology is introduced. Based on this topology on the Euclidean space, a flow generated from a linear differential equation is proved to be Li–Yorke chaotic under certain conditions, which is in sharp contract to the well-known fact that linear differential equations cannot be chaotic in a finite-dimensional space with a strong topology.\",\"PeriodicalId\":340975,\"journal\":{\"name\":\"Chaos: An Interdisciplinary Journal of Nonlinear Science\",\"volume\":\"180 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos: An Interdisciplinary Journal of Nonlinear Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0163463\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos: An Interdisciplinary Journal of Nonlinear Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/5.0163463","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Li–Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology
Li–Yorke chaos of linear differential equations in a finite-dimensional space with a weak topology is introduced. Based on this topology on the Euclidean space, a flow generated from a linear differential equation is proved to be Li–Yorke chaotic under certain conditions, which is in sharp contract to the well-known fact that linear differential equations cannot be chaotic in a finite-dimensional space with a strong topology.
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