A KAM theorem for finitely differentiable Hamiltonian systems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Koudjinan, C. E.¹ 

[1] Univ Roma Tre, Dipartimento Matemat & Fis, Largo SL Murialdo 1, I-00146 Rome, Italy

关键词: Nearly integrable Hamiltonian systems;    KAM theory;    Smooth KAM tori;    Arnold?s scheme;    Cantor-like set;    Smoothing techniques;   

DOI  :  10.1016/j.jde.2020.03.044

来源: Elsevier

【 摘 要 】

Given / > 2v > 2d > 4, we prove the persistence of a Cantor family of KAM tori of measure 0 (E1/2 v/) for any non degenerate nearly integrable Hamiltonian system of class C/ (g x Td), where v 1 is the Diophantine power of the frequencies of the persistent KAM tori and gr C Rd is a bounded domain, provided that the sizes of the perturbation is sufficiently small. This extends a result by D. Salamon in [25] according to which we do have the persistence of a single KAM torus in the same framework. Moreover, as for the persistence of a single torus, the regularity assumption is essentially optimal. 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free