On the stability of equilibria in two-degrees-of-freedom Hamiltonian systems under resonances

被引：16

作者：

Elipe, A ^{[1
]}

Lanchares, V

Pascual, AI

机构：

[1] Univ Zaragoza, Grp Mecan Espacial, E-50009 Zaragoza, Spain

[2] Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain

来源：

JOURNAL OF NONLINEAR SCIENCE | 2005年 / 15卷 / 05期

关键词：

nonlinear stability; normal forms;

D O I：

10.1007/s00332-004-0674-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem of stability of equilibrium points in Hamiltonian systems of two degrees of freedom under resonances. Determining the stability or instability is based on a geometrical criterion based on how two surfaces, related with the normal form, intersect one another. The equivalence of this criterion with a result of Cabral and Meyer is proved. With this geometrical procedure, the hypothesis may be extended to more general cases.

引用

页码：305 / 319

页数：15

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