期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 33, 期 6, 页码 2593-2619出版社
AMER INST MATHEMATICAL SCIENCES
DOI: 10.3934/dcds.2013.33.2593
关键词
Quasi-periodic systems; KAM-iteration; Diophantine conditions; hyperbolic equilibrium point
资金
- National Natural Science Foundation of China [11071038]
- Natural Science Foundation of Jiangsu Province [BK2010420]
In this paper we consider two-dimensional nonlinear quasi-periodic system with small perturbations. Assume that the unperturbed system has a hyperbolic-type degenerate equilibrium point and the frequency satisfies the Diophantine conditions. Using the KAM iteration we prove that for sufficiently small perturbations, the system can be reduced by a nonlinear quasi-periodic transformation to a suitable normal form with an equilibrium point at the origin. Hence, for the system we can obtain a small quasi-periodic solution.
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