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arXiv · 0808.0866

Constant-length substitutions and countable scrambled sets

François Blanchard·Fabien Durand·Alejandro Maass
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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.

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François Blanchard, Fabien Durand, Alejandro Maass. 2008-08-06. Constant-length substitutions and countable scrambled sets. https://doi.org/10.1088/0951-7715%2F17%2F3%2F005

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