Resonance conjecture via weak KAM theory

被引：3

作者：

Niu, Xun ^{[1
]}

Wang, Kaizhi ^{[2
]}

Li, Yong ^{[1
,3
]}

机构：

[1] Jilin Univ, Inst Math, Changchun 130012, Peoples R China

[2] Shanghai Jiao Tong Univ, CMA Shanghai, Sch Math Sci, Shanghai 200240, Peoples R China

[3] Northeast Normal Univ, Sch Math & Stat, Ctr Math & Interdisciplinary Sci, Changchun 130024, Peoples R China

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2023年 / 172卷

关键词：

Resonance conjecture; Weak KAM theory; Viscosity solutions; LOWER-DIMENSIONAL TORI; MINIMIZING MEASURES; INVARIANT TORI; PDE METHODS; PERTURBATIONS; PSEUDOGRAPHS; CONVERGENCE; EQUATIONS;

D O I：

10.1016/j.matpur.2023.01.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Poincare established the problem how much of the stability mechanism of integrable Hamiltonian systems can persist under small perturbations, which he called "the fundamental problem of dynamics". This paper deals with the fundamental problem in general resonant case. We give a weak KAM type result that for each y in the g (with rank m0)-resonant surface, the nearly integrable Hamiltonian system has at least m0 + 1 weak KAM solutions associated with relative equilibria. (c) 2023 Elsevier Masson SAS. All rights reserved.

引用

页码：139 / 163

页数：25

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