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Regul. Chaotic Dyn., 2015, Volume 20, Issue 2, Pages 184–188 (Mi rcd52)  

This article is cited in 3 scientific papers (total in 3 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

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

DOI: https://doi.org/10.1134/S1560354715020069

References: PDF file   HTML file

Bibliographic databases:

MSC: 54H20, 37B20, 54C56
Received: 04.04.2014
Language:

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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\by Nikita Shekutkovski
\paper One Property of Components of a Chain Recurrent Set
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 2
\pages 184--188
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. Shekutkovski, “Intrinsic shape - the proximate approach”, Filomat, 29:10 (2015), 2199–2205  crossref  mathscinet  zmath  isi  scopus
    2. N. Shekutkovski, M. Shoptrajanov, “Intrinsic shape of the chain recurrent set”, Topology Appl., 202 (2016), 117–126  crossref  mathscinet  zmath  isi  scopus
    3. N. Shekutkovski, M. Shoptrajanov, “Intrinsic Shape Property of Global Attractors in Metrizable Spaces”, Nelineinaya dinam., 16:1 (2020), 181–194  mathnet  crossref  elib
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