Constant-length substitutions and countable scrambled sets
arXiv:0808.0866 · doi:10.1088/0951-7715/17/3/005
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.