de Mathématiques de Luminy
Blanchard François, Durand
Fabien, Maass Alejandro.
Constant-lenght substitutions and countable scrambled sets.
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-lenght substitution dynamical systems. Starting from a circle rotation we also construct a dynamical system having Li-Yorke pairs, none of which is recurrent.