Resonant tori of arbitrary codimension for quasi-periodically forced systems

被引：18
|
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.
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页数：21
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