{"title":"Shadowing as a structural property of the space of dynamical systems","authors":"J. Meddaugh","doi":"10.3934/dcds.2021197","DOIUrl":null,"url":null,"abstract":"We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate that, for this class of spaces, in order to determine whether a system has shadowing, it is sufficient to check that continuously generated pseudo-orbits can be shadowed.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete & Continuous Dynamical Systems - S","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcds.2021197","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate that, for this class of spaces, in order to determine whether a system has shadowing, it is sufficient to check that continuously generated pseudo-orbits can be shadowed.
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