The existence of quasiperiodic solutions for coupled Duffing-type equations

被引：3

作者：

Jin, Huiping ^{[2
]}

Liu, Bin ^{[3
]}

Wang, Yiqian ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[2] Yiwu Ind & Commercial Coll, Yiwu 322000, Zhejiang, Peoples R China

[3] Peking Univ, Sch Math, Beijing 100871, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 374卷 / 02期

关键词：

Hamiltonian system; Quasiperiodic solutions; Scale change; Small twist theorem; Canonical transformation; INVARIANT TORI; NONLINEAR OSCILLATIONS; LAGRANGE STABILITY; BOUNDEDNESS; POTENTIALS; THEOREM;

D O I：

10.1016/j.jmaa.2010.08.027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the existence of infinitely many quasiperiodic solutions for a class of coupled Duffing-type equations via RAM theorem. Moreover, the set of quasiperiodic solutions is of infinitely Lebesgue measure in the phase space. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：429 / 441

页数：13

共 21 条

[1]

Dieckerhoff R., 1987, Ann. Della Scuola Normale Superiore di Pisa-Classe di Scienze, V14, P79

[2] On the application of KAM theory to discontinuous dynamical systems [J].

Kunze, M ;

Kupper, T ;

You, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 139 (01) :1-21

[3] INVARIANT CURVES AND TIME-DEPENDENT POTENTIALS [J].

LAEDERICH, S ;

LEVI, M .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1991, 11 :365-378

[4]

LEVI M, 1992, DYNAMIC REPORTED, V1

[5] Lagrangian stability of a nonlinear quasi-periodic system [J].

Lin, SS ;

Wang, YQ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 293 (01) :258-268

[6]

Littlewood J.E., 1968, Some problems in real and complex analysis

[7]

LITTLEWOOD JE, 1966, J LONDON MATH SOC, V41, P491

[8] Boundedness of solutions for semilinear Duffing equations [J].

Liu, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 145 (01) :119-144

[9] Boundedness in nonlinear oscillations at resonance [J].

Liu, B .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 153 (01) :142-174

[10] Invariant tori in nonlinear oscillations [J].

Liu, B ;

Wang, YQ .

SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 1999, 42 (10) :1047-1058

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