{"title":"Dichotomies for Triangular Systems via Admissibility","authors":"Davor Dragičević, Kenneth J. Palmer","doi":"10.1007/s10884-023-10335-6","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"55 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10884-023-10335-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.
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