Reducibility of a class of 2k-dimensional Hamiltonian systems with quasi-periodic coefficients. Issue 3 (3rd July 2019) - Li, Jia; Su, Youhui; Shi, Yanling
ABSTRACT: In this paper, we consider the following real analytic Hamiltonian system x ˙ = ( A + ε Q ( t, ε ) ) x, x ∈ R 2 k, where A is a constant Hamiltonian matrix with the different eigenvalues ± w 1 − 1, ± λ 2, …, ± λ k, where w 1 ∈ R, ± λ i ≠ 0 for 2 ≤ i ≤ k are real, and Q ( t, ε ) is quasi-periodic with frequencies w 1, w 2, … w r . Without any non-degeneracy condition with respect to ϵ, we prove that by a quasi-periodic symplectic mapping, then for most of the sufficiently small parameter ϵ, the Hamiltonian system is reducible.