Admissibility and nonuniform polynomial dichotomies

TL;DR

This paper characterizes polynomial dichotomies in nonautonomous linear dynamics through admissibility of solutions and demonstrates their robustness, extending the understanding of stability in such systems.

Contribution

It introduces a complete characterization of polynomial dichotomies via admissibility and proves their robustness in nonuniform settings.

Findings

Polynomial dichotomies are characterized by admissibility conditions.

The robustness of nonuniform polynomial dichotomies is established.

The results apply to general one-sided nonautonomous dynamics.

Abstract

For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of a polynomial dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility of bounded solutions. As a nontrivial application, we establish the robustness of the notion of a nonuniform polynomial dichotomy.