{"title":"Two-sided delay-difference equations and evolution maps","authors":"Luís Barreira, Claudia Valls","doi":"10.1007/s00010-024-01121-w","DOIUrl":null,"url":null,"abstract":"<p>We establish the equivalence of hyperbolicity and of two other properties for a two-sided linear delay-difference equation and its evolution map. These two properties are the admissibility with respect to various pairs of spaces, and the Ulam–Hyers stability of the equation, again with respect to various spaces. This gives characterizations of important properties of a linear dynamical system in terms of corresponding properties of the autonomous dynamical system determined by the associated evolution map.</p>","PeriodicalId":55611,"journal":{"name":"Aequationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Aequationes Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00010-024-01121-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We establish the equivalence of hyperbolicity and of two other properties for a two-sided linear delay-difference equation and its evolution map. These two properties are the admissibility with respect to various pairs of spaces, and the Ulam–Hyers stability of the equation, again with respect to various spaces. This gives characterizations of important properties of a linear dynamical system in terms of corresponding properties of the autonomous dynamical system determined by the associated evolution map.
期刊介绍：
aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.
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