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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 2, Pages 184–188
DOI: https://doi.org/10.1134/S1560354715020069 (Mi rcd52) 		 
This article is cited in 5 scientific papers (total in 5 papers)

One Property of Components of a Chain Recurrent Set

Nikita Shekutkovski

Institute of Mathematics, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius University, 1000 Skopje, Republic of Macedonia
Citations (5)
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DOI: https://doi.org/10.1134/S1560354715020069
Abstract: For flows defined on a compact manifold with or without boundary, it is shown that the connectivity components of a chain recurrent set possess a stronger connectivity known as joinability (or pointed 1-movability in the sense of Borsuk). As a consequence, the Vietoris–van Dantzig solenoid cannot be a component of a chain recurrent set, although the solenoid appears as a minimal set of a flow.
Keywords: chain recurrent set, continuity in a covering, pointed 1-movability, joinability.
Received: 04.04.2014
Bibliographic databases:
Document Type: Article
MSC: 54H20, 37B20, 54C56
Language: English
Citation: Nikita Shekutkovski, “One Property of Components of a Chain Recurrent Set”, Regul. Chaotic Dyn., 20:2 (2015), 184–188
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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