Robustness of discrete dynamics via Lyapunov sequences (Q1048044)

This paper is concerned with nonuniform exponential dichotomy, a generalization of (uniform) exponential dichotomy, which was disucssed for ordinary differential equations so much in past years. In this paper the authors consider it for a nonautonomous dynamics with discrete time defined by a sequence of matrices. They give a complete characterization of nonuniform exponential contractions and nonuniform exponential dichotomies in terms of Lyapunov sequences. They also obtain inverse theorems that give explicitly Lyapunov sequences for a given contraction or dichotomy. They establish the robustness under sufficiently small linear perturbations both of nonuniform exponential contractions and nonuniform exponential dichotomies.