Exponential Splitting for Nonautonomous Linear Discrete-Time Systems in Banach Spaces

TL;DR

This paper explores generalized exponential splitting concepts for nonautonomous linear discrete-time systems in Banach spaces, extending classical exponential dichotomies and illustrating their distinctions through examples.

Contribution

It introduces generalized exponential splitting concepts for nonautonomous systems, expanding the theoretical framework beyond classical exponential dichotomies.

Findings

Connections between different exponential splitting concepts are established.

Examples demonstrate that these concepts are distinct.

The generalizations encompass well-known exponential dichotomies.

Abstract

In this paper we consider some concepts of exponential splitting for nonautonomous linear discrete-time systems. These concepts are generalizations of some well-known concepts of (uniform and nonuniform) exponential dichotomies. Connections between these concepts are presented and some illustrating examples prove that these are distinct.