Constant-length substitutions and countable scrambled sets

Details Constant-length substitutions and countable scrambled sets Constant-length substitutions and countable scrambled sets

2008-08-06

arxiv.org/abs/0808.0866v1

Nonlinearity 17 (2004) 817-833

Mathematics

Dynamical Systems

Scientific paper

10.1088/0951-7715/17/3/005

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.

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