{"title":"A C^1 Arnol'd-Liouville theorem","authors":"M. Arnaud, Jinxin Xue","doi":"10.24033/ast.1109","DOIUrl":null,"url":null,"abstract":"In this paper, we prove a version of Arnol'd-Liouville theorem for C 1 commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori is crucial to determine the Dynamics on each Lagrangian torus and that the C 1 regularity of the foliation by invariant Lagrangian tori is crucial to prove the continuity of Arnol'd-Liouville coordinates. We also explore various notions of C 0 and Lipschitz integrability.","PeriodicalId":55445,"journal":{"name":"Asterisque","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asterisque","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.24033/ast.1109","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: 6
Abstract
In this paper, we prove a version of Arnol'd-Liouville theorem for C 1 commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori is crucial to determine the Dynamics on each Lagrangian torus and that the C 1 regularity of the foliation by invariant Lagrangian tori is crucial to prove the continuity of Arnol'd-Liouville coordinates. We also explore various notions of C 0 and Lipschitz integrability.
期刊介绍：
The publications part of the site of the French Mathematical Society (Société Mathématique de France - SMF) is bilingual English-French. You may visit the pages below to discover our list of journals and book collections. The institutional web site of the SMF (news, teaching activities, conference announcements...) is essentially written in French.
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
