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[1] Li Jia, Zhu Chunpeng,. On reducibility of a class of nonlinear quasi-periodic systemswith small perturbational parameters near equilibrium [J]. Journal of Southeast University (English Edition), 2012, 28 (2): 256-260. [doi:10.3969/j.issn.1003-7985.2012.02.022]
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On reducibility of a class of nonlinear quasi-periodic systemswith small perturbational parameters near equilibrium()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
28
Issue:
2012 2
Page:
256-260
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2012-06-30

Info

Title:
On reducibility of a class of nonlinear quasi-periodic systemswith small perturbational parameters near equilibrium
Author(s):
Li Jia1 2 Zhu Chunpeng2
1Department of Mathematics, Southeast University, Nanjing 211189, China
2Mathematics and Physical Sciences Technology, Xuzhou Institute of Technology, Xuzhou 221008, China
Keywords:
quasi-periodic reducible non-resonance condition non-degeneracy condition KAM iteration
PACS:
O175.15
DOI:
10.3969/j.issn.1003-7985.2012.02.022
Abstract:
Consider the reducibility of a class of nonlinear quasi-periodic systems with multiple eigenvalues under perturbational hypothesis in the neighborhood of equilibrium. That is, consider the following system(·overx)=(A+εQ(t))x+εg(t)+h(x, t), where A is a constant matrix with multiple eigenvalues; h=O(x2)(x→0); and h(x, t), Q(t), and g(t)are analytic quasi-periodic with respect to t with the same frequencies. Under suitable hypotheses of non-resonance conditions and non-degeneracy conditions, for most sufficiently small ε, the system can be reducible to a nonlinear quasi-periodic system with an equilibrium point by means of a quasi-periodic transformation.

References:

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Memo

Memo:
Biography: Li Jia(1983—), female, graduate, lijia831112@163.com.
Citation: Li Jia, Zhu Chunpeng.On reducibility of a class of nonlinear quasi-periodic systems with small perturbational parameters near equilibrium[J].Journal of Southeast University(English Edition), 2012, 28(2):256-260.[doi:10.3969/j.issn.1003-7985.2012.02.022]
Last Update: 2012-06-20