Global smooth linearization of nonautonomous contractions on Banach spaces

Abstract

The main purpose of this paper is to establish a global smooth linearization result for two classes of nonautonomous dynamics with discrete time. More precisely, we consider a nonlinear and nonautonomous dynamics given by a two-sided sequence of maps as well as variational systems whose linear part is contractive, and under suitable assumptions we construct C 1 conjugacies between the original dynamics and its linear part. We stress that our dynamics acts on a arbitrary Banach space. Our arguments rely on related results dealing with autonomous dynamics.