On Local Aspects of Topological Weak Mixing, Sequence Entropy and Chaos
نویسندگان
چکیده
In this paper we show that for every n ≥ 2 there are minimal systems with perfect weakly mixing sets of order n and all weakly mixing sets of order n+1 trivial. We present some relations between weakly mixing sets and topological sequence entropy, in particular, we prove that invertible minimal systems with nontrivial weakly mixing sets of order 3 always have positive topological sequence entropy. We also study relations between weak mixing of sets and other well established notions from qualitative theory of dynamical systems like (regional) proximality, chaos and equicontinuity in broad sense.
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