三或多自由度哈密顿系统周期轨道划分曲面的推广- IV

M. Katsanikas, S. Wiggins
{"title":"三或多自由度哈密顿系统周期轨道划分曲面的推广- IV","authors":"M. Katsanikas, S. Wiggins","doi":"10.1142/s0218127423300203","DOIUrl":null,"url":null,"abstract":"Recently, we presented two methods of constructing periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom [Katsanikas & Wiggins, 2021a, 2021b]. These methods were illustrated with an application to a quadratic normal form Hamiltonian system with three degrees of freedom. More precisely, in these papers we constructed a section of the dividing surfaces that intersect with the hypersurface [Formula: see text]. This was motivated by studies in reaction dynamics since in this model reaction occurs when the sign of the [Formula: see text] coordinate changes. In this paper, we continue the work of the third paper [Katsanikas & Wiggins, 2023] of this series of papers to construct the full dividing surfaces that are obtained by our algorithms and to prove the no-recrossing property. In the third paper we did this for the dividing surfaces of the first method [Katsanikas & Wiggins, 2021a]. Now we are doing the same for the dividing surfaces of the second method [Katsanikas & Wiggins, 2021b]. In addition, we computed the dividing surfaces of the second method for a coupled case of the quadratic normal form Hamiltonian system and we compared our results with those of the uncoupled case. This paper completes this series of papers about the construction of periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":"37 1","pages":"2330020:1-2330020:10"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Generalization of the Periodic Orbit Dividing Surface for Hamiltonian Systems with Three or More Degrees of Freedom - IV\",\"authors\":\"M. Katsanikas, S. Wiggins\",\"doi\":\"10.1142/s0218127423300203\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recently, we presented two methods of constructing periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom [Katsanikas & Wiggins, 2021a, 2021b]. These methods were illustrated with an application to a quadratic normal form Hamiltonian system with three degrees of freedom. More precisely, in these papers we constructed a section of the dividing surfaces that intersect with the hypersurface [Formula: see text]. This was motivated by studies in reaction dynamics since in this model reaction occurs when the sign of the [Formula: see text] coordinate changes. In this paper, we continue the work of the third paper [Katsanikas & Wiggins, 2023] of this series of papers to construct the full dividing surfaces that are obtained by our algorithms and to prove the no-recrossing property. In the third paper we did this for the dividing surfaces of the first method [Katsanikas & Wiggins, 2021a]. Now we are doing the same for the dividing surfaces of the second method [Katsanikas & Wiggins, 2021b]. In addition, we computed the dividing surfaces of the second method for a coupled case of the quadratic normal form Hamiltonian system and we compared our results with those of the uncoupled case. This paper completes this series of papers about the construction of periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom.\",\"PeriodicalId\":13688,\"journal\":{\"name\":\"Int. J. Bifurc. Chaos\",\"volume\":\"37 1\",\"pages\":\"2330020:1-2330020:10\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Int. J. Bifurc. Chaos\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218127423300203\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Bifurc. Chaos","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218127423300203","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

最近,我们提出了两种构造具有三个或更多自由度的哈密顿系统的周期轨道划分曲面的方法[Katsanikas & Wiggins, 2021a, 2021b]。并以一个具有三自由度的二次型正规哈密顿系统为例说明了这些方法。更准确地说,在这些论文中,我们构造了与超曲面相交的分割曲面的一部分[公式:见文本]。这是出于对反应动力学的研究,因为在这个模型中,当[公式:见正文]坐标的符号发生变化时,反应就会发生。在本文中,我们继续了本系列论文的第三篇论文[Katsanikas & Wiggins, 2023]的工作,构造了由我们的算法得到的全分曲面,并证明了不重交的性质。在第三篇论文中,我们对第一种方法的划分面进行了这样的处理[Katsanikas & Wiggins, 2021a]。现在我们对第二种方法的分割面做同样的事情[Katsanikas & Wiggins, 2021b]。此外,我们还计算了二次型正规哈密顿系统耦合情况下第二种方法的分度曲面,并与未耦合情况下的分度曲面进行了比较。本文完成了具有三个或更多自由度的哈密顿系统的周期分轨曲面的构造。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Generalization of the Periodic Orbit Dividing Surface for Hamiltonian Systems with Three or More Degrees of Freedom - IV
Recently, we presented two methods of constructing periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom [Katsanikas & Wiggins, 2021a, 2021b]. These methods were illustrated with an application to a quadratic normal form Hamiltonian system with three degrees of freedom. More precisely, in these papers we constructed a section of the dividing surfaces that intersect with the hypersurface [Formula: see text]. This was motivated by studies in reaction dynamics since in this model reaction occurs when the sign of the [Formula: see text] coordinate changes. In this paper, we continue the work of the third paper [Katsanikas & Wiggins, 2023] of this series of papers to construct the full dividing surfaces that are obtained by our algorithms and to prove the no-recrossing property. In the third paper we did this for the dividing surfaces of the first method [Katsanikas & Wiggins, 2021a]. Now we are doing the same for the dividing surfaces of the second method [Katsanikas & Wiggins, 2021b]. In addition, we computed the dividing surfaces of the second method for a coupled case of the quadratic normal form Hamiltonian system and we compared our results with those of the uncoupled case. This paper completes this series of papers about the construction of periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom.
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
0
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信