{"title":"三维系统的动力学特性与能量-卡西米尔映射图像之间的联系","authors":"Mingxing Xu, Shaoyun Shi, Kaiyin Huang","doi":"10.3934/dcds.2023126","DOIUrl":null,"url":null,"abstract":"We investigate the connection between the dynamical properties of a class of 3D systems and the geometric characteristics of the image of the energy-Casimir mapping. By examining the energy-Casimir mapping for such systems, we can explore the stability of the equilibrium states, the distribution of the periodic solutions, and the existence of homoclinic or heteroclinic orbits. We apply our findings to investigate the dynamic behavior of two specific equations, and provide a topological classification of the fibers of the energy-Casimir mapping for the two systems.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"26 1","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The connection between the dynamical properties of 3D systems and the image of the energy-Casimir mapping\",\"authors\":\"Mingxing Xu, Shaoyun Shi, Kaiyin Huang\",\"doi\":\"10.3934/dcds.2023126\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We investigate the connection between the dynamical properties of a class of 3D systems and the geometric characteristics of the image of the energy-Casimir mapping. By examining the energy-Casimir mapping for such systems, we can explore the stability of the equilibrium states, the distribution of the periodic solutions, and the existence of homoclinic or heteroclinic orbits. We apply our findings to investigate the dynamic behavior of two specific equations, and provide a topological classification of the fibers of the energy-Casimir mapping for the two systems.\",\"PeriodicalId\":51007,\"journal\":{\"name\":\"Discrete and Continuous Dynamical Systems\",\"volume\":\"26 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete and Continuous Dynamical Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/dcds.2023126\",\"RegionNum\":3,\"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":"Discrete and Continuous Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcds.2023126","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The connection between the dynamical properties of 3D systems and the image of the energy-Casimir mapping
We investigate the connection between the dynamical properties of a class of 3D systems and the geometric characteristics of the image of the energy-Casimir mapping. By examining the energy-Casimir mapping for such systems, we can explore the stability of the equilibrium states, the distribution of the periodic solutions, and the existence of homoclinic or heteroclinic orbits. We apply our findings to investigate the dynamic behavior of two specific equations, and provide a topological classification of the fibers of the energy-Casimir mapping for the two systems.
期刊介绍：
DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.
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