A HARTMAN-GROBMAN THEOREM FOR ALGEBRAIC DICHOTOMIES

Abstract

Algebraic dichotomy is a generalization of an exponential dichotomy (see Lin [28]). 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 homeomorphism in the linearization theorem is Hölder continuous (and has a Hölder continuous inverse). Comparing with exponential dichotomy, algebraic dichotomy is more complicate. The exponential dichotomy leads us to the estimates (Formula Presented) and (Formula Presented) which are convergent. However, the algebraic dichotomy will leads us to (Formula Presented), whose the convergence is unknown in the sense of Riemann.