{"title":"Average shadowing and gluing property","authors":"Michael Blank","doi":"10.1112/mtk.12187","DOIUrl":null,"url":null,"abstract":"<p>The purpose of this work is threefold: (i) extend shadowing theory for discontinuous and non-invertible systems, (ii) consider more general classes of perturbations (for example, small only on average), (iii) establish a general theory based on the property that the shadowing holds for the case of a single perturbation. The “gluing” construction used in the analysis of the last property turns out to be the key point of this theory.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12187","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: 4
Abstract
The purpose of this work is threefold: (i) extend shadowing theory for discontinuous and non-invertible systems, (ii) consider more general classes of perturbations (for example, small only on average), (iii) establish a general theory based on the property that the shadowing holds for the case of a single perturbation. The “gluing” construction used in the analysis of the last property turns out to be the key point of this theory.
期刊介绍：
Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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