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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Published in | Acta mathematica Sinica. English series Vol. 28; no. 4; pp. 801 - 816 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Heidelberg
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
01.04.2012
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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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 |