Robusteness of discrete nonuniform dichotomic behavior

TL;DR

This paper proves that a broad class of dichotomic behaviors in nonautonomous linear difference equations in Banach spaces remain stable under small linear perturbations, extending and improving existing robustness results.

Contribution

It introduces a new approach to establish robustness of discrete nonuniform dichotomic behavior, covering more general cases and providing improved theorems.

Findings

Robustness of dichotomic behavior under small perturbations

New theorems improve previous results in the literature

Dichotomic behavior remains essentially unchanged up to a constant factor

Abstract

For nonautonomous linear difference equations in Banach spaces we show that a very general type of dichotomic behavior persists under small enough additive linear perturbations. By using a new approach, we obtain two general robustness theorems that improve several results in the literature and also contain new situations. In particular, unlike several existent results for particular growth rates, we show that, up to a multiplicative constant, the dichotomic behavior for the perturbed equation is the same as the one for the original equation.