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

Published online by Cambridge University Press:  06 March 2018

MATÚŠ DIRBÁK Open the ORCID record for MATÚŠ DIRBÁK [Opens in a new window] ,
ROMAN HRIC ,
PETER MALIČKÝ ,
L’UBOMÍR SNOHA  and
VLADIMÍR ŠPITALSKÝ
MATÚŠ DIRBÁK
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia email Matus.Dirbak@umb.sk, Roman.Hric@umb.sk, Peter.Malicky@umb.sk, Lubomir.Snoha@umb.sk, Vladimir.Spitalsky@umb.sk
ROMAN HRIC
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia email Matus.Dirbak@umb.sk, Roman.Hric@umb.sk, Peter.Malicky@umb.sk, Lubomir.Snoha@umb.sk, Vladimir.Spitalsky@umb.sk
PETER MALIČKÝ
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia email Matus.Dirbak@umb.sk, Roman.Hric@umb.sk, Peter.Malicky@umb.sk, Lubomir.Snoha@umb.sk, Vladimir.Spitalsky@umb.sk
L’UBOMÍR SNOHA
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia email Matus.Dirbak@umb.sk, Roman.Hric@umb.sk, Peter.Malicky@umb.sk, Lubomir.Snoha@umb.sk, Vladimir.Spitalsky@umb.sk
VLADIMÍR ŠPITALSKÝ
Affiliation:
Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovského 40, 974 01 Banská Bystrica, Slovakia email Matus.Dirbak@umb.sk, Roman.Hric@umb.sk, Peter.Malicky@umb.sk, Lubomir.Snoha@umb.sk, Vladimir.Spitalsky@umb.sk
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Abstract

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.

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 11 , November 2019 , pp. 2968 - 2982
Copyright
© Cambridge University Press, 2018 

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