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Minimal self-joinings and positive topological entropy. (English) Zbl 0859.54027

The authors’ abstract: “We show that the properties of almost minimal self-joinings and strong almost minimal self-joinings, introduced by A. del Junco in Topological Dynamics [Ergodic Theory Dyn. Syst. 7, 211-227 (1987; Zbl 0635.54020)], are compatible with positive topological entropy, as opposed to the stronger property of minimal self-joinings. This is done both by proving existence theorems and by explicitly constructing some symbolic systems having these properties, which are modifications of the Chacón system. It is shown furthermore that these systems have no non-trivial factors with completely positive topological entropy”.

MSC:

54H20 Topological dynamics (MSC2010)
28D05 Measure-preserving transformations
54C70 Entropy in general topology

Citations:

Zbl 0635.54020
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References:

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