Resonance conjecture via weak KAM theory

被引：1

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

共 50 条

[1] AN INFINITE-DIMENSIONAL WEAK KAM THEORY VIA RANDOM VARIABLES
Gomes, Diogo
Nurbekyan, Levon
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (11) : 6167 - 6185
[2] New Identities for Weak KAM Theory
Evans, Lawrence Craig
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2017, 38 (02) : 379 - 392
[3] Weak KAM theory for potential MFG
Cardaliaguet, Pierre
Masoero, Marco
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (07) : 3255 - 3298
[4] New identities for Weak KAM theory
Lawrence Craig Evans
[J]. Chinese Annals of Mathematics, Series B, 2017, 38 : 379 - 392
[5] Towards a quantum analog of weak KAM theory
Evans, LC
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 244 (02) : 311 - 334
[6] Towards weak KAM theory at relative equilibrium
Niu, Xun
Ji, Shuguan
Li, Yong
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2024, 392 : 325 - 363
[7] Further PDE methods for weak KAM theory
Lawrence C. Evans
[J]. Calculus of Variations and Partial Differential Equations, 2009, 35 : 435 - 462
[8] Towards a Quantum Analog of Weak KAM Theory
Lawrence C. Evans
[J]. Communications in Mathematical Physics, 2004, 244 : 311 - 334
[9] Regularization of Subsolutions in Discrete Weak KAM Theory
Bernard, Patrick
Zavidovique, Maxime
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2013, 65 (04): : 740 - 756
[10] Weak KAM theory and partial differential equations
Evans, Lawrence C.
[J]. CALCULUS OF VARIATIONS AND NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 1927 : 123 - 154

← 1 2 3 4 5 →