{"title":"拉格朗日系统-周期轨迹的希尔公式","authors":"M. Davletshin","doi":"10.1090/S0077-1554-2014-00213-2","DOIUrl":null,"url":null,"abstract":"In this paper some results of a work by Bolotin and Treshchëv are generalized to the case of g-periodic trajectories of Lagrangian systems. Formulae connecting the characteristic polynomial of the monodromy matrix with the determinant of the Hessian of the action functional are obtained both for the discrete and continuous cases. Applications to the problem of stability of g-periodic trajectories are given. Hill’s formula can be used to study g-periodic orbits obtained by variational methods. §","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":"74 1","pages":"65-96"},"PeriodicalIF":0.0000,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00213-2","citationCount":"3","resultStr":"{\"title\":\"Hill’s formula for -periodic trajectories of Lagrangian systems\",\"authors\":\"M. Davletshin\",\"doi\":\"10.1090/S0077-1554-2014-00213-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper some results of a work by Bolotin and Treshchëv are generalized to the case of g-periodic trajectories of Lagrangian systems. Formulae connecting the characteristic polynomial of the monodromy matrix with the determinant of the Hessian of the action functional are obtained both for the discrete and continuous cases. Applications to the problem of stability of g-periodic trajectories are given. Hill’s formula can be used to study g-periodic orbits obtained by variational methods. §\",\"PeriodicalId\":37924,\"journal\":{\"name\":\"Transactions of the Moscow Mathematical Society\",\"volume\":\"74 1\",\"pages\":\"65-96\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1090/S0077-1554-2014-00213-2\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the Moscow Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/S0077-1554-2014-00213-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Moscow Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/S0077-1554-2014-00213-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
Hill’s formula for -periodic trajectories of Lagrangian systems
In this paper some results of a work by Bolotin and Treshchëv are generalized to the case of g-periodic trajectories of Lagrangian systems. Formulae connecting the characteristic polynomial of the monodromy matrix with the determinant of the Hessian of the action functional are obtained both for the discrete and continuous cases. Applications to the problem of stability of g-periodic trajectories are given. Hill’s formula can be used to study g-periodic orbits obtained by variational methods. §
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