A C1 ARNOL'D-LIOUVILLE THEOREM

被引：3

作者：

Arnaud, Marie-Claude ^{[1
]}

Xue, Jinxin ^{[2
,3
]}

机构：

[1] Univ Paris, Sorbonne Univ, CNRS, Inst Math Jussieu Paris Rive Gauche, F-75013 Paris, France

[2] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

[3] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

来源：

ASTERISQUE | 2020年 / 416期

关键词：

(C-0-)Poisson commutativity; Hamiltonian; Arnol'd- Liouville theorem; foliation; Lagrangian submanifolds; generating functions; symplectic homeomorphisms; complete integrability; REGULARITY;

D O I：

10.24033/ast.1109

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove a version of Arnol'd-Liouville theorem for C-2 Hamiltonians having enough 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.

引用

页码：1 / 31

页数：31

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