Admissibility and generalized nonuniform dichotomies for discrete\n dynamics

2020/12/22 by César M. Silva, Silva, César M. · 1 citation
Mathematics · Engineering · #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2012.11910

Abstract

We obtain characterizations of nonuniform dichotomies, defined by general\ngrowth rates, based on admissibility conditions. Additionally, we use the\nobtained characterizations to derive robustness results for the considered\ndichotomies. As particular cases, we recover several results in the literature\nconcerning nonuniform exponential dichotomies and nonuniform polynomial\ndichotomies as well as new results for nonuniform dichotomies with logarithmic\ngrowth.\n

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