{"title":"流动的相干测度和光滑Lyapunov 1型的存在性","authors":"Janko Latschev","doi":"10.1016/j.top.2006.01.001","DOIUrl":null,"url":null,"abstract":"<div><p>Let a smooth vector field <span><math><mi>V</mi></math></span> on a smooth closed manifold <span><math><mi>M</mi></math></span> be given and let <span><math><mi>Z</mi><mo>⊂</mo><mi>M</mi></math></span> be an isolated invariant set for the flow of <span><math><mi>V</mi></math></span>. In this situation, we give a necessary and sufficient condition for the existence of a Lyapunov 1-form for <span><math><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>Z</mi><mo>)</mo></mrow></math></span> in terms of the relative asymptotic cycles associated with certain invariant measures of the flow.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 4","pages":"Pages 707-723"},"PeriodicalIF":0.0000,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.01.001","citationCount":"6","resultStr":"{\"title\":\"Coherent measures and the existence of smooth Lyapunov 1-forms for flows\",\"authors\":\"Janko Latschev\",\"doi\":\"10.1016/j.top.2006.01.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let a smooth vector field <span><math><mi>V</mi></math></span> on a smooth closed manifold <span><math><mi>M</mi></math></span> be given and let <span><math><mi>Z</mi><mo>⊂</mo><mi>M</mi></math></span> be an isolated invariant set for the flow of <span><math><mi>V</mi></math></span>. In this situation, we give a necessary and sufficient condition for the existence of a Lyapunov 1-form for <span><math><mrow><mo>(</mo><mi>V</mi><mo>,</mo><mi>Z</mi><mo>)</mo></mrow></math></span> in terms of the relative asymptotic cycles associated with certain invariant measures of the flow.</p></div>\",\"PeriodicalId\":54424,\"journal\":{\"name\":\"Topology\",\"volume\":\"45 4\",\"pages\":\"Pages 707-723\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.top.2006.01.001\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0040938306000073\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040938306000073","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Coherent measures and the existence of smooth Lyapunov 1-forms for flows
Let a smooth vector field on a smooth closed manifold be given and let be an isolated invariant set for the flow of . In this situation, we give a necessary and sufficient condition for the existence of a Lyapunov 1-form for in terms of the relative asymptotic cycles associated with certain invariant measures of the flow.
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