Constant-length substitutions and countable scrambled sets

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.

Cited by in corpus (7)

• On weak mixing, minimality and weak disjointness of all iterates
• Automorphisms of automatic shifts
• Necessary and sufficient conditions for a dynamical system to be topologically conjugate to a given substitution minimal system
• For graph maps, one scrambled pair implies Li-Yorke chaos
• Morphisms, Symbolic sequences, and their Standard Forms
• Decidability of the isomorphism problem between multidimensional substitutive subshifts
• Topological chaos: what may this mean ?