Persistence of lower dimensional tori of general types in Hamiltonian systems

被引：53

作者：

Li, Y ^{[1
]}

Yi, YF

机构：

[1] Jilin Univ, Dept Math, Changchun 130012, Peoples R China

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2005年 / 357卷 / 04期

关键词：

Hamiltonian systems; invariant tori; KAM theory; Melnikov problem; persistence;

D O I：

10.1090/S0002-9947-04-03564-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This work is a generalization to a result of J. You (1999). We study the persistence of lower dimensional tori of general type in Hamiltonian systems of general normal forms. By introducing a modified linear KAM iterative scheme to deal with small divisors, we shall prove a persistence result, under a Melnikov type of non-resonance condition, which particularly allows multiple and degenerate normal frequencies of the unperturbed lower dimensional tori.

引用

页码：1565 / 1600

页数：36