On the Effective Reducibility of a Class of Quasi-Periodic Linear Hamiltonian Systems Close to Constant Coefficients. (2nd September 2018)

• Record Type: Journal Article
• Authors: Xue, Nina; Zhao, Wencai
• Other Names: Wang Liguang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2018(2018)
• Publication Date: 2018-09-02
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2018/5189873
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we consider the effective reducibility of the quasi-periodic linear Hamiltonian systemx ˙ = A + ε Q t, ε x, ε ∈ 0, ε 0, whereA is a constant matrix with possible multiple eigenvalues andQ ( t, ε ) is analytic quasi-periodic with respect tot . Under nonresonant conditions, it is proved that this system can be reduced toy ˙ = A ⁎ ε + ε R ⁎ t, ε y, ε ∈ 0, ε ⁎, whereR ⁎ is exponentially small inε, and the change of variables that perform such a reduction is also quasi-periodic with the same basic frequencies asQ .