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A weakly mixing dynamical system with the whole space being a transitive extremal distributionally scrambled set. (English) Zbl 1351.37061

Summary: It is known that the whole space can be a Li-Yorke scrambled set in a compact dynamical system, but this does not hold for distributional chaos. In this paper we construct a noncompact weekly mixing dynamical system, and prove that the whole space is a transitive extremal distributionally scrambled set in this system.

MSC:

37B20 Notions of recurrence and recurrent behavior in topological dynamical systems
37A25 Ergodicity, mixing, rates of mixing
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