通过克雷格-韦恩-布尔干方法论 KAM Tori 的线性稳定性

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-05-24 DOI:10.1137/22m1512958

Xiaolong He, Jia Shi, Yunfeng Shi, Xiaoping Yuan

{"title":"通过克雷格-韦恩-布尔干方法论 KAM Tori 的线性稳定性","authors":"Xiaolong He, Jia Shi, Yunfeng Shi, Xiaoping Yuan","doi":"10.1137/22m1512958","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3605-3645, June 2024. <br/> Abstract. In this paper, we revisit the Melnikov’s persistency problem and illustrate that the Craig–Wayne–Bourgain method can be strengthened to obtain both the existence and linear stability of the invariant tori. The proof is free from the second Melnikov’s condition.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Linear Stability of KAM Tori via the Craig–Wayne–Bourgain Method\",\"authors\":\"Xiaolong He, Jia Shi, Yunfeng Shi, Xiaoping Yuan\",\"doi\":\"10.1137/22m1512958\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3605-3645, June 2024. <br/> Abstract. In this paper, we revisit the Melnikov’s persistency problem and illustrate that the Craig–Wayne–Bourgain method can be strengthened to obtain both the existence and linear stability of the invariant tori. The proof is free from the second Melnikov’s condition.\",\"PeriodicalId\":51150,\"journal\":{\"name\":\"SIAM Journal on Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Mathematical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/22m1512958\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/22m1512958","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷第 3 期，第 3605-3645 页，2024 年 6 月。摘要在本文中，我们重温了梅尔尼科夫的持久性问题，并说明克雷格-韦恩-布尔干函数方法可以被加强以获得不变环的存在性和线性稳定性。证明不受梅尔尼科夫第二条件的限制。

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

On Linear Stability of KAM Tori via the Craig–Wayne–Bourgain Method

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3605-3645, June 2024.
Abstract. In this paper, we revisit the Melnikov’s persistency problem and illustrate that the Craig–Wayne–Bourgain method can be strengthened to obtain both the existence and linear stability of the invariant tori. The proof is free from the second Melnikov’s condition.

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

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.