UNA NOTA SOBRE EL PRE-PRINT: “ON THE GROBMAN-HARTMAN THEOREM IN α-HÖLDER CLASS FOR BANACH SPACES”

Abstract

A well-known theorem in discrete nonlinear dynamics due to Grobman \cite{Grobman} and Hartman \cite{Hartman} tells us that a diffeomorphism of class C¹, F:E --> E, with E Banach space and p a hyperbolic fixed point can be topologically conjugated to a linear diffeomorphism Λ=DF(p) (in a neighborhood of p). This work aims to fill in all the gaps and complete the proofs found in the pre-print by Belintskii- Rayskin, where it gives the existence of a conjugation Hölder continuous of the Grobman-Hartman theorem. Finally, we will give an example to illustrate our result.