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