Invariant scrambled sets, uniform rigidity and weak mixing
Dynamical Systems
2016-06-01 v1
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 -scrambled set for some 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.
Cite
@article{arxiv.1410.7118,
title = {Invariant scrambled sets, uniform rigidity and weak mixing},
author = {Magdalena Foryś and Wen Huang and Jian Li and Piotr Oprocha},
journal= {arXiv preprint arXiv:1410.7118},
year = {2016}
}
Comments
17 pages, to appear in Israel Journal of Mathematics