Jie Li, Piotr Oprocha, Xiangdong Ye, Ruifeng Zhang
Published 2015-04-30Version 1
In the paper we study relations of rigidity, equicontinuity and pointwise recurrence between a t.d.s. $(X,T)$ and the t.d.s. $(K(X),T_K)$ induced on the hyperspace $K(X)$ of all compact subsets of $X$, and provide some characterizations. Among other examples, we construct a minimal, non-equicontinuous, distal and uniformly rigid t.d.s. and a t.d.s. which has dense small periodic sets but does not have dense distal points, solving that way open questions existing in the literature.
On problems of Danzer and Gowers and dynamics on the space of closed subsets of $\mathbb{R}^d$
Transitive points via Furstenberg family
Equivalent conditions of Devaney chaos on the hyperspace
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