Smoothness of Class $$C^2$$ of Nonautonomous Linearization Without Spectral Conditions

Abstract

We prove that smoothness of nonautonomous linearization is of class \(C^2.\) Our approach admits the existence of stable and unstable manifolds determined by a family of nonautonomous hyperbolicities, including the non uniform exponential case, while for the classic exponential dichotomy we obtain the same class of differentiability except for a zero Lebesgue measure set. Moreover, our goal is reached without spectral conditions.