Abstract
In this article we study the relationship between the exponential dichotomy properties of a triangular system of linear difference equations and its associated diagonal system. We use admissibility to give new shorter proofs of results obtained in Battelli et al. (J Differ Equ Appl 28:1054–1086, 2022) and we also establish new necessary and sufficient conditions that the diagonal system have a dichotomy when the triangular system has a dichotomy. We conclude with analogous results for differential equations.
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Funding
D.D. was supported in part by Croatian Science Foundation under the Project IP-2019-04-1239 and by the University of Rijeka under the Projects uniri-prirod-18-9 and uniri-prprirod-19-16.
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Dragičević, D., Palmer, K.J. Dichotomies for Triangular Systems via Admissibility. J Dyn Diff Equat (2024). https://doi.org/10.1007/s10884-023-10335-6
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DOI: https://doi.org/10.1007/s10884-023-10335-6