{"title":"A KAM Theorem for the Time Quasi-periodic Reversible Perturbations of Linear Wave Equations Beyond Brjuno Conditions","authors":"","doi":"10.1007/s10884-024-10360-z","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>This paper is concerned with the existence of quasi-periodic response solutions (i.e., solutions that are quasi-periodic with the same frequencies as forcing term) for a class of forced reversible wave equations with derivative nonlinearity. The forcing frequency <span> <span>\\(\\omega \\in \\mathbb {R}^2\\)</span> </span> would be Liouvillean which is weaker than the usual Diophantine and Brjuno conditions. The derivative nonlinearity in the equation also leads to some difficulty in measure estimate. To overcome it, we also use the Töplitz–Lipschitz property of vector field. The proof is based on an infinite dimensional Kolmogorov–Arnold–Moser theorem for reversible systems.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"22 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10884-024-10360-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with the existence of quasi-periodic response solutions (i.e., solutions that are quasi-periodic with the same frequencies as forcing term) for a class of forced reversible wave equations with derivative nonlinearity. The forcing frequency \(\omega \in \mathbb {R}^2\) would be Liouvillean which is weaker than the usual Diophantine and Brjuno conditions. The derivative nonlinearity in the equation also leads to some difficulty in measure estimate. To overcome it, we also use the Töplitz–Lipschitz property of vector field. The proof is based on an infinite dimensional Kolmogorov–Arnold–Moser theorem for reversible systems.
期刊介绍：
Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
