Resumen de Reducibility for a Class of Nonlinear Quasi-Periodic Systems under Brjuno-Russmann’s Non-resonance Conditions

Chunpeng Zhu, Jia Li

• This paper studies the following analytic quasi-periodic nonlinear system x˙ = (A + εQ(t, ε))x + εg(t, ε) + h(x, t, ε), where A is a constant matrix and h = O(x2). We prove that under Brjuno-Russmann’s non-resonance conditions and non-degeneracy conditions, for most small enough parameter ε, this nonlinear system is reducible by a quasi-periodic mapping.