$C^1$ Smoothness of the Conjugacy in a Delayed Nonautonomous Hartman--Grobman Theorem via $\mu$-Dichotomies

Abstract

We investigate the differentiability of the conjugacy in a nonautonomous version of the Hartman--Grobman Theorem for systems with finite delay, where the linear part satisfies a $\mu$-dichotomy. Under suitable conditions on the nonlinear perturbation, the conjugacy is shown to be a $C^1$ diffeomorphism.