Robusteness of discrete nonuniform dichotomic behavior

2013/08/30 by António J. G. Bento, Bento, António J. G., César M. Silva +1
Engineering · Mathematics · Medicine · #34D09 #37B55 #39A30 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1308.6820

openalex publication_date 2013/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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