On Polynomial Dichotomies of Discrete Nonautonomous Systems on the Half-Line

The aim of this paper is to provide new characterizations for polynomial dichotomies of discrete nonautonomous systems on the half-line. First, we establish equivalent structures for the ranges of projections for a polynomial dichotomy with respect to a sequence of norms. Next, we establish the conn...

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Bibliographic Details
Published in:Carpathian Journal of Mathematics 2022-01, Vol.38 (3), p.663-680
Main Authors: Dragičević, Davor, Sasu, Adina Luminiţa, Sasu, Bogdan
Format: Article
Language:English
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Dedicated to Prof. Emeritus Mihail Megan on the occasion of his 75th anniversary
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Summary:The aim of this paper is to provide new characterizations for polynomial dichotomies of discrete nonautonomous systems on the half-line. First, we establish equivalent structures for the ranges of projections for a polynomial dichotomy with respect to a sequence of norms. Next, we establish the connections between polynomial dichotomies and other dichotomic behaviors. We obtain for the first time a characterization of polynomial dichotomy with respect to a sequence of norms in terms of ordinary dichotomy and exponential dichotomy of suitable systems with respect to well-chosen sequences of norms. The results are obtained in the most general case, without any additional assumptions regarding the coefficients of the underlying systems.
ISSN:1584-2851
1843-4401
DOI:10.37193/CJM.2022.03.12