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.
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}
}