Foryś, Magdalena; Huang, Wen; Li, Jian; Oprocha, Piotr Invariant scrambled sets, uniform rigidity and weak mixing. (English) Zbl 1359.37021 Isr. J. Math. 211, 447-472 (2016). Summary: We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant \(\delta\)-scrambled set for some \(\delta >0\) if and only if it has a fixed point and is not uniformly rigid. We also provide two methods for the construction of completely scrambled systems which are weakly mixing, proximal and uniformly rigid. Cited in 1 ReviewCited in 9 Documents MSC: 37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) 37B20 Notions of recurrence and recurrent behavior in topological dynamical systems 37A25 Ergodicity, mixing, rates of mixing 54H20 Topological dynamics (MSC2010) Keywords:transitive dynamical system; scrambled set; weakly mixing × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Akin, E., Lectures on Cantor and Mycielski sets for dynamical systems, No. 356, 21-79 (2004), Providence, RI · Zbl 1064.37015 · doi:10.1090/conm/356/06496 [2] Akin, E.; Auslander, J.; Berg, K., When is a transitive map chaotic?, No. 5, 25-40 (1996), Berlin · Zbl 0861.54034 [3] E. Akin and E. Glasner, Residual properties and almost equicontinuity, Journal d’Analyse Mathématique 84 (2001), 243-286. · Zbl 1182.37009 · doi:10.1007/BF02788112 [4] E. Akin and S. 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