Quasi-periodic stability of normally resonant tori

PHYSICA D-NONLINEAR PHENOMENA

卷:238

Article

Broer, Henk W.²  Ciocci, M. Cristina¹  Hanssmann, Heinz³  Vanderbauwhede, Andre⁴ 

[1] Univ Coll W Flanders, Dept PIH, B-8500 Kortrijk, Belgium

[2] Univ Groningen, Dept Math & Comp Sci, NL-9700 AK Groningen, Netherlands

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

[4] Univ Ghent, Dept Pure Math & Comp Algebra, B-9000 Ghent, Belgium

关键词: Kolmogorov-Arnold-Moser theory;    Quasi-periodic stability;    Normal-internal resonance;    Covering space;    Preservation of structure;    Reversibility;    Equivariance;   

DOI  :  10.1016/j.physd.2008.10.004

来源: Elsevier

【 摘 要 】

We study quasi-periodic tori under a normal-internal resonance, possibly with multiple eigenvalues. Two non-degeneracy conditions play a role. The first of these generalizes invertibility of the Floquet matrix and prevents drift of the lower dimensional torus. The second condition involves a Kolmogorov-like variation of the internal frequencies and simultaneously versality of the Floquet matrix unfolding. We focus on the reversible setting, but our results carry over to the Hamiltonian and dissipative contexts. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free