Resonant tori of arbitrary codimension for quasi-periodically forced systems

被引：20

作者：

Corsi, Livia ^{[1
]}

Gentile, Guido ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, 686 Cherry St NW, Atlanta, GA 30332 USA

[2] Univ Roma Tre, Dipartimento Matemat & Fis, I-00146 Rome, Italy

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2017年 / 24卷 / 01期

基金：

欧洲研究理事会;

关键词：

INTEGRABLE HAMILTONIAN-SYSTEMS; LOWER-DIMENSIONAL TORI; INVARIANT TORI; KAM THEOREM;

D O I：

10.1007/s00030-016-0425-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a system of rotators subject to a small quasi periodic forcing. We require the forcing to be analytic and satisfy a time reversibility property and we assume its frequency vector to be Bryuno. Then we prove that, without imposing any non-degeneracy condition on the forcing, there exists at least one quasi-periodic solution with the same frequency vector as the forcing. The result can be interpreted as a theorem of persistence of lower-dimensional tori of arbitrary codimension in degenerate cases.

引用

页数：21

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