α-Hölder Linearization

A well known theorem of Hartman and Grobman says that aC2diffeomorphismf: Rn→Rnwith a hyperbolic fixed point at 0 can be topologically conjugated to the linear diffeomorphismL=df(0) (in a neighborhood of 0). On the other hand, if a non-planar map has resonance, then linearization may not beC1. A counter-example is due to P. Hartman (see [H2]). In this paper we will show that for anyα (0, 1) there exists anα-Hölder linearization in a neighborhood of 0 for the counterexample of Hartman. No resonance condition will be required. A linearization of a more general map will be discussed.