One Property of Components of a Chain Recurrent Set

    2015, Volume 20, Number 2, pp.  184-188

    Author(s): Shekutkovski N.

    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
    Citation: Shekutkovski N., One Property of Components of a Chain Recurrent Set, Regular and Chaotic Dynamics, 2015, Volume 20, Number 2, pp. 184-188

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