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arXiv · 1410.7118

Invariant scrambled sets, uniform rigidity and weak mixing

Magdalena Foryś·Wen Huang·Jian Li·Piotr Oprocha
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Abstract

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 $δ$-scrambled set for some $δ>0$ if and only if it has a fixed point and not uniformly rigid. We also provide two methods for the construction of completely scrambled systems which are weakly mixing, proximal and uniformly rigid.

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Magdalena Foryś, Wen Huang, Jian Li, Piotr Oprocha. 2014-10-27. Invariant scrambled sets, uniform rigidity and weak mixing. https://doi.org/10.1007/s11856-015-1278-1

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