The Stability of the Elliptic Equilibrium of Planar Quasi-periodic Hamiltonian Systems

In this paper, we study the planar Hamiltonian systemwhere where f is real analytic in x and θ,A（θ） is a 2×2real analytic symmetric matrix,J=（1^-1） and w is a Diophantine vector. Under the assumption that the unperturbed system reducible and stable, we obtain a series of criteria for the stability a...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 28; no. 4; pp. 801 - 816
Main Authors Wu, Yun Chao, Wang, Yi Qian
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.04.2012
Springer Nature B.V
Subjects
Criteria
Equilibrium
Instability
Mathematical analysis
Mathematics
Mathematics and Statistics
Stability
Studies
Systems science
Vectors (mathematics)
准周期
哈密顿系统
对称矩阵
平衡
平面
摄动系统
椭圆
稳定性
Lyapunov stability
elliptic equilibrium
quasi-periodic system
37J25
Hamiltonian system
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Summary:In this paper, we study the planar Hamiltonian systemwhere where f is real analytic in x and θ,A（θ） is a 2×2real analytic symmetric matrix,J=（1^-1） and w is a Diophantine vector. Under the assumption that the unperturbed system reducible and stable, we obtain a series of criteria for the stability and instability of the equilibrium of the perturbed system.
Bibliography:In this paper, we study the planar Hamiltonian systemwhere where f is real analytic in x and θ,A（θ） is a 2×2real analytic symmetric matrix,J=（1^-1） and w is a Diophantine vector. Under the assumption that the unperturbed system reducible and stable, we obtain a series of criteria for the stability and instability of the equilibrium of the perturbed system.
11-2039/O1
Lyapunov stability, elliptic equilibrium, Hamiltonian system, quasi-periodic system
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-0006-y