一个全局Hartman-Grobman定理

Commun. Inf. Syst. Pub Date : 2020-02-14 DOI:10.4310/cis.2022.v22.n1.a2

Xiaochang A. Wang, Jiexin Dai

{"title":"一个全局Hartman-Grobman定理","authors":"Xiaochang A. Wang, Jiexin Dai","doi":"10.4310/cis.2022.v22.n1.a2","DOIUrl":null,"url":null,"abstract":"We showed that for any bounded neighborhood of a hyperbolic equilibrium point $x_0$, there is a transformation which is locally homeomorphism, such that the system is changed into a linear system in this neighborhood. \nIf the eigenvalues of $Df(x_0)$ are all located in the left-half complex plane, then there is a homeomorphism on the whole region of attraction such that the nonlinear system on the region of attraction is changed into a linear system under such a coordinate change.","PeriodicalId":185710,"journal":{"name":"Commun. Inf. Syst.","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A global Hartman-Grobman theorem\",\"authors\":\"Xiaochang A. Wang, Jiexin Dai\",\"doi\":\"10.4310/cis.2022.v22.n1.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We showed that for any bounded neighborhood of a hyperbolic equilibrium point $x_0$, there is a transformation which is locally homeomorphism, such that the system is changed into a linear system in this neighborhood. \\nIf the eigenvalues of $Df(x_0)$ are all located in the left-half complex plane, then there is a homeomorphism on the whole region of attraction such that the nonlinear system on the region of attraction is changed into a linear system under such a coordinate change.\",\"PeriodicalId\":185710,\"journal\":{\"name\":\"Commun. Inf. Syst.\",\"volume\":\"21 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Commun. Inf. Syst.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/cis.2022.v22.n1.a2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Commun. Inf. Syst.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/cis.2022.v22.n1.a2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 2

摘要

我们证明了对于双曲平衡点$x_0$的任何有界邻域，存在一个局部同纯的变换，使得系统在这个邻域内变成一个线性系统。如果$Df(x_0)$的特征值都位于复平面的左半部分，则在整个引力区域上存在同纯性，使得在这样的坐标变化下，引力区域上的非线性系统变为线性系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A global Hartman-Grobman theorem

We showed that for any bounded neighborhood of a hyperbolic equilibrium point $x_0$, there is a transformation which is locally homeomorphism, such that the system is changed into a linear system in this neighborhood. If the eigenvalues of $Df(x_0)$ are all located in the left-half complex plane, then there is a homeomorphism on the whole region of attraction such that the nonlinear system on the region of attraction is changed into a linear system under such a coordinate change.

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

Commun. Inf. Syst.

自引率

0.00%

发文量