Reducibility of ultra‐differentiable quasi‐periodic linear systems

Abstract In ultra‐differentiable classes, this paper studies the reducibility of the quasi‐periodic linear system , where is a constant matrix with different eigenvalues , is a ultra‐differentiable quasi‐periodic matrix with basic frequencies and is a small perturbation parameter. Suppose that the set formed by the eigenvalues of A and the basic frequencies of Q satisfies a non‐resonant condition. Then, it is proved that the linear system can be conjugated to a constant system by a quasi‐periodic change of variables.