English

When all closed subsets are recurrent?

Dynamical Systems 2015-05-01 v1

Abstract

In the paper we study relations of rigidity, equicontinuity and pointwise recurrence between a t.d.s. (X,T)(X,T) and the t.d.s. (K(X),TK)(K(X),T_K) induced on the hyperspace K(X)K(X) of all compact subsets of XX, 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.

Keywords

Cite

@article{arxiv.1504.08191,
  title  = {When all closed subsets are recurrent?},
  author = {Jie Li and Piotr Oprocha and Xiangdong Ye and Ruifeng Zhang},
  journal= {arXiv preprint arXiv:1504.08191},
  year   = {2015}
}

Comments

30 pages

R2 v1 2026-06-22T09:25:45.326Z