Persistence of lower dimensional invariant tori in a class of reversible systems. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Hong, Weiwei; Zhang, Dongfeng
• Is Part Of: Dynamical systems. Volume 33:Issue 1(2018)
• Page Start: 72
• Page End: 92
• Publication Date: 2018-01-02
• Subjects: Reversible system -- Hamiltonian system -- invariant tori -- KAM iteration -- non-degeneracy condition; 37J40 -- 47A55 -- 70K43; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2017.1298725
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: In this paper we prove the persistence of lower dimensional invariant tori for a class of reversible systems without any non-degeneracy condition. In the proof, we use the special nature that the dimension of the frequency ω is 2 and the modified KAM iteration to prove the persistence of lower dimensional hyperbolic invariant tori, but the frequency has some small shifts from small perturbations.