On the linearization theorem for nonautonomous differential equations

This paper presents an improvement of Palmer's linearization theorem in [10]. Palmer's linearization theorem extended the Hartman–Grobman theorem to the nonautonomous case. It requires two essential conditions: (i) the nonlinear term is bounded and Lipschitzian; (ii) the linear system as a whole possesses an exponential dichotomy. The main purpose of this paper is to weaken assumptions (i) and (ii). Also in this paper we prove that the topologically equivalent function H(t,x)H(t,x) in the linearization theorem is always Hölder continuous (and has a Hölder continuous inverse), so as a result we generalize and improve Palmer's linearization theorem.