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.
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Shekutkovski, N. One property of components of a chain recurrent set. Regul. Chaot. Dyn. 20, 184–188 (2015). https://doi.org/10.1134/S1560354715020069
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DOI: https://doi.org/10.1134/S1560354715020069