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Topological sequence entropy and chaos of star maps. (English) Zbl 1181.37013

Summary: Let \(X_n = \{z\in\mathbb{C}: z^n\in [0, 1]\}\), \(n\in \mathbb{N}\), and let \(f: X_n\to X_n\) be a continuous map such that \(f (0) = 0\). In this paper we prove that \(f\) is chaotic in the sense of Li-Yorke iff there is a strictly increasing sequence of positive integers \(A\) such that the topological sequence entropy of \(f\) relative to \(A\) is positive.

MSC:

37B40 Topological entropy
37E25 Dynamical systems involving maps of trees and graphs
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