English

Constant-length substitutions and countable scrambled sets

Dynamical Systems 2009-11-13 v1

Abstract

In this paper we provide examples of topological dynamical systems having either finite or countable scrambled sets. In particular we study conditions for the existence of Li-Yorke, asymptotic and distal pairs in constant--length substitution dynamical systems. Starting from a circle rotation we also construct a dynamical system having Li--Yorke pairs, none of which is recurrent.

Keywords

Cite

@article{arxiv.0808.0866,
  title  = {Constant-length substitutions and countable scrambled sets},
  author = {François Blanchard and Fabien Durand and Alejandro Maass},
  journal= {arXiv preprint arXiv:0808.0866},
  year   = {2009}
}
R2 v1 2026-06-21T11:08:08.547Z