哈密顿动力系统与三维曲面几何

T. Bayrakdar, A. A. Ergin
{"title":"哈密顿动力系统与三维曲面几何","authors":"T. Bayrakdar, A. A. Ergin","doi":"10.1080/1726037X.2017.1390847","DOIUrl":null,"url":null,"abstract":"Abstract Hamiltonian vector field, Poisson vector field and the gradient of Hamiltonian function defines Darboux frame along an integral curve of a Hamiltonian dynamical system on a surface whose normal vector field corresponds to the Poisson structure for a given Hamiltonian system. We show that the existence of compatible Poisson structures determined by the normal legs of the Darboux frame is resolved to the characteristic equation for the Weingarten map. We also show that a Hamiltonian dynamical system in three dimensions has bi-Hamiltonian representation determined by the normal legs of Frenet-Serret triad if and only if an integral curve of Hamiltonian vector field is both a geodesic and a line of curvature.","PeriodicalId":42788,"journal":{"name":"Journal of Dynamical Systems and Geometric Theories","volume":"15 1","pages":"163 - 176"},"PeriodicalIF":0.4000,"publicationDate":"2017-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/1726037X.2017.1390847","citationCount":"0","resultStr":"{\"title\":\"Hamiltonian dynamical systems and geometry of surfaces in 3-D\",\"authors\":\"T. Bayrakdar, A. A. Ergin\",\"doi\":\"10.1080/1726037X.2017.1390847\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Hamiltonian vector field, Poisson vector field and the gradient of Hamiltonian function defines Darboux frame along an integral curve of a Hamiltonian dynamical system on a surface whose normal vector field corresponds to the Poisson structure for a given Hamiltonian system. We show that the existence of compatible Poisson structures determined by the normal legs of the Darboux frame is resolved to the characteristic equation for the Weingarten map. We also show that a Hamiltonian dynamical system in three dimensions has bi-Hamiltonian representation determined by the normal legs of Frenet-Serret triad if and only if an integral curve of Hamiltonian vector field is both a geodesic and a line of curvature.\",\"PeriodicalId\":42788,\"journal\":{\"name\":\"Journal of Dynamical Systems and Geometric Theories\",\"volume\":\"15 1\",\"pages\":\"163 - 176\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2017-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/1726037X.2017.1390847\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamical Systems and Geometric Theories\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/1726037X.2017.1390847\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamical Systems and Geometric Theories","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/1726037X.2017.1390847","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

在法向量场对应于给定哈密顿系统泊松结构的曲面上,哈密顿矢量场、泊松矢量场和哈密顿函数的梯度沿哈密顿动力系统的积分曲线定义了Darboux系。我们证明了相容泊松结构的存在性是由达布坐标系的法向支决定的,它被分解为Weingarten图的特征方程。我们还证明了三维哈密顿动力系统具有由Frenet-Serret三角法向支决定的双哈密顿表示,当且仅当哈密顿矢量场的积分曲线既是测地线又是曲率线。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Hamiltonian dynamical systems and geometry of surfaces in 3-D
Abstract Hamiltonian vector field, Poisson vector field and the gradient of Hamiltonian function defines Darboux frame along an integral curve of a Hamiltonian dynamical system on a surface whose normal vector field corresponds to the Poisson structure for a given Hamiltonian system. We show that the existence of compatible Poisson structures determined by the normal legs of the Darboux frame is resolved to the characteristic equation for the Weingarten map. We also show that a Hamiltonian dynamical system in three dimensions has bi-Hamiltonian representation determined by the normal legs of Frenet-Serret triad if and only if an integral curve of Hamiltonian vector field is both a geodesic and a line of curvature.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
7
期刊最新文献
Geometrical Aspects of Motion of Charged Particles in Magnetic and Killing Magnetic Fields and Their Corresponding Trajectories in Anti-De Sitter 3-Space Geometric Structures On 3-Dimensional Hom-Lie Algebras Almost Kenmotsu Manifolds Admitting Certain Critical Metric Study of Frw Type Kaluza-Klein Domain Wall Cosmological Models in the Presence of Massive Scalar Field in a Modified Gravity Analysis of Resonant Curve and Phase Portrait Due to Earth’s Equatorial Ellipticity In the Earth-Moon System Using Perturbation Technique
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1