Constant-length substitutions and countable scrambled sets

François Blanchard (1) , Fabien Durand (2) , Alejandro Maass (3)

1 IML - Institut de mathématiques de Luminy
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
3 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

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 cons\-tant--length substitution dynamical systems. Starting from a circle rotation we also construct a dynamical system having Li--Yorke pairs, none of which is recurrent.

Mots clés: li-yorke; pairs; chaos; substitution; constant length

Domaines: Systèmes dynamiques [math.DS]

François Blanchard, Fabien Durand, Alejandro Maass. Constant-length substitutions and countable scrambled sets. Nonlinearity, 2004, 17, pp.817-833. ⟨hal-00309506⟩