A Hartman-Grobman theorem for algebraic dichotomies

Abstract

Algebraic dichotomy is a generalization of an exponential dichotomy (see Lin [1]). This paper gives a version of Hartman-Grobman linearization theorem assuming that linear system admits an algebraic dichotomy, which generalizes the Palmer's linearization theorem. Besides, we prove that the equivalent function H(t, x) in the linearization theorem is Hölder continuous (and has a Hölder continuous inverse).