{"title":"A TOPOLOGICAL INVARIANT AND A CRITERION FOR THE EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM","authors":"A. Fomenko, Kh Tsishang","doi":"10.1070/IM1991V036N03ABEH002035","DOIUrl":null,"url":null,"abstract":"A new topological invariant is constructed which classifies integrable Hamiltonian systems with two degrees of freedom (admitting a Bott integral). A criterion for the equivalence of Bott systems is proved: such systems are topologically equivalent if and only if their topological invariants coincide. The topological invariant is effectively calculated for specific integrable Hamiltonian systems in physics and mechanics.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"24 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"134","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1991V036N03ABEH002035","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 134
Abstract
A new topological invariant is constructed which classifies integrable Hamiltonian systems with two degrees of freedom (admitting a Bott integral). A criterion for the equivalence of Bott systems is proved: such systems are topologically equivalent if and only if their topological invariants coincide. The topological invariant is effectively calculated for specific integrable Hamiltonian systems in physics and mechanics.
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