Admissibility and generalized nonuniform dichotomies for discrete dynamics

César M. Silva

doi:10.3934/cpaa.2021112

Article Contents

2021, Volume 20, Issue 10: 3419-3443. Doi: 10.3934/cpaa.2021112 open access

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Admissibility and generalized nonuniform dichotomies for discrete dynamics

César M. Silva

Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001 Covilhã, Portugal

Received: January 2021

Revised: May 2021

Early access: June 2021

Published: October 2021

The author was partially supported by FCT through CMUBI (project UIDB/MAT/00212/2020)

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Abstract

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

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Mathematics Subject Classification: Primary: 34D09, 37D25.

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