Minimality for actions of abelian semigroups on compact spaces with a free interval

Minimality for actions of abelian semigroups on compact spaces with a free interval

We study minimality for continuous actions of abelian semigroups on compact Hausdorff spaces with a free interval. First, we give a necessary and sufficient condition for such a space to admit a minimal action of a given abelian semigroup. Further, for actions of abelian semigroups we provide a tric...

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Veröffentlicht in:Ergodic theory and dynamical systems 2019-11, Vol.39 (11), p.2968-2982
Hauptverfasser: DIRBÁK, MATÚŠ, HRIC, ROMAN, MALIČKÝ, PETER, SNOHA, L’UBOMÍR, ŠPITALSKÝ, VLADIMÍR
Format: Artikel
Sprache:eng
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Semigroups
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Zusammenfassung:We study minimality for continuous actions of abelian semigroups on compact Hausdorff spaces with a free interval. First, we give a necessary and sufficient condition for such a space to admit a minimal action of a given abelian semigroup. Further, for actions of abelian semigroups we provide a trichotomy for the topological structure of minimal sets intersecting a free interval.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2018.4