A C^1 Arnol'd-Liouville theorem

IF 1 4区数学 Q1 MATHEMATICS

Asterisque Pub Date : 2016-12-23 DOI:10.24033/ast.1109

M. Arnaud, Jinxin Xue

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.

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C^1阿诺-刘维尔定理

在本文中，我们证明了c1可交换哈密顿量的Arnol'd-Liouville定理的一个版本。我们证明了不变拉格朗日环面叶化的Lipschitz正则性对于确定每个拉格朗日环面上的动力学是至关重要的，而不变拉格朗日环面叶化的c1正则性对于证明Arnol'd-Liouville坐标的连续性是至关重要的。我们还探讨了c0和Lipschitz可积性的各种概念。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Asterisque MATHEMATICS-

CiteScore

2.90

自引率

0.00%

发文量

审稿时长

>12 weeks

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