Stability of equilibrium solutions of autonomous and periodic Hamiltonian systems in the case of multiple resonances

被引:11
作者
dos Santos, F. [1 ]
Vidal, C. [2 ]
机构
[1] Univ Fed Sergipe, Dept Matemat, Sao Cristovao, SE, Brazil
[2] Univ Bio Bio, Fac Ciencias, Dept Matemat, Concepcion, Chile
关键词
Hamiltonian system; Equilibrium solutions; Stability; Lie's normal form; Multiple resonance; SINGLE RESONANCE;
D O I
10.1016/j.jde.2015.01.044
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we give necessary conditions for Lie-stability of the equilibrium solutions of autonomous and periodic Hamiltonian systems with n degrees of freedom which possess multiple resonances of arbitrary order. Necessary conditions for instability in the sense of Lyapunov in some cases of multiple resonances are provided. These conditions depend on the order of the resonance and the coefficients of the Hamiltonian function. (c) 2015 Elsevier Inc. All rights reserved.
引用
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页码:3880 / 3901
页数:22
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