{"title":"仿射流的链式递推和塞尔格拉德定理","authors":"Fritz Colonius, Alexandre J. Santana","doi":"10.1007/s10884-024-10351-0","DOIUrl":null,"url":null,"abstract":"<p>Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade’s theorem is determined. The results are illustrated by an application to affine control systems with bounded control range.\n</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"71 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Chain Recurrence and Selgrade’s Theorem for Affine Flows\",\"authors\":\"Fritz Colonius, Alexandre J. Santana\",\"doi\":\"10.1007/s10884-024-10351-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade’s theorem is determined. The results are illustrated by an application to affine control systems with bounded control range.\\n</p>\",\"PeriodicalId\":15624,\"journal\":{\"name\":\"Journal of Dynamics and Differential Equations\",\"volume\":\"71 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamics and Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10884-024-10351-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10884-024-10351-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Chain Recurrence and Selgrade’s Theorem for Affine Flows
Affine flows on vector bundles with chain transitive base flow are lifted to linear flows and the decomposition into exponentially separated subbundles provided by Selgrade’s theorem is determined. The results are illustrated by an application to affine control systems with bounded control range.
期刊介绍：
Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.
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