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A characterization of \(\omega\)-limit sets of maps of the interval with zero topological entropy. (English) Zbl 0788.58021
Let \(I\) be the unit interval [0,1] and let \(W \subset(0,1)\) be infinite and compact. Then the following conditions are equivalent: (1) \(W\) is an \(\omega\)-limit set of some map \(f \in C(I,I)\) with zero topological entropy. (2) \(W=Q \cup P\), where \(Q\) is a Cantor set and \(P\) is empty or a countably infinite set, disjoint with \(Q\) and such that: (a) every interval contiguous to \(Q\) contains at most two points of \(P\), (b) each of the intervals \([0,\min Q]\), \([\max Q,1]\) contains at most one point of \(P\), (c) \(\text{cl} (P)=Q \cup P\).
Reviewer: J.Ombach (Kraków)

MSC:
37E99 Low-dimensional dynamical systems
54C70 Entropy in general topology
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