Quasi-periodic solutions and stability of the equilibrium for quasi-periodically forced planar reversible and Hamiltonian systems under the Bruno condition

被引：12

作者：

Hanssmann, Heinz ^{[2
]}

Si, Jianguo ^{[1
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China

[2] Univ Utrecht, Inst Math, NL-3508 TA Utrecht, Netherlands

来源：

NONLINEARITY | 2010年 / 23卷 / 03期

基金：

中国国家自然科学基金;

关键词：

FIXED-POINTS; GERMS; DIFFEOMORPHISMS; LINEARIZATION;

D O I：

10.1088/0951-7715/23/3/007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the existence of quasi-periodic solutions of non-autonomous two-dimensional reversible and Hamiltonian systems under the Bruno condition. As an application we study the dynamical stability of the trivial solution at the origin of a quasi-periodically forced planar system. Under a mild non-degeneracy condition we give a criterion that is necessary and sufficient for a large class of systems.

引用

页码：555 / 577

页数：23

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