{"title":"关于刘维尔公式的推广","authors":"Zhengyong Zhou, L. Xie","doi":"10.7153/DEA-09-17","DOIUrl":null,"url":null,"abstract":"In this article, we obtain a new formula which generalizes the Liouville formula of the linear differential system to nonlinear differential system. We establish the relationship between the Jacobi determinant of the first integral and the trace of Jacobi matrix of the n -dimensional vector field.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"123 1","pages":"213-217"},"PeriodicalIF":0.0000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a generalization of the Liouville formula\",\"authors\":\"Zhengyong Zhou, L. Xie\",\"doi\":\"10.7153/DEA-09-17\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we obtain a new formula which generalizes the Liouville formula of the linear differential system to nonlinear differential system. We establish the relationship between the Jacobi determinant of the first integral and the trace of Jacobi matrix of the n -dimensional vector field.\",\"PeriodicalId\":11162,\"journal\":{\"name\":\"Differential Equations and Applications\",\"volume\":\"123 1\",\"pages\":\"213-217\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/DEA-09-17\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/DEA-09-17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this article, we obtain a new formula which generalizes the Liouville formula of the linear differential system to nonlinear differential system. We establish the relationship between the Jacobi determinant of the first integral and the trace of Jacobi matrix of the n -dimensional vector field.
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