Substitutions, tiling dynamical systems and minimal self-joinings

2014/02/23 by Y. G. Son, Younghwan Son, Son, Younghwan · 1 citation
Computer Science · Mathematics · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #math.DS #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1402.5672

arxiv created 2014/02/23 · arxiv updated 2014/02/25

Abstract

We investigate substitution subshifts and tiling dynamical systems arising from the substitutions (1) θ: 0 → 001,1 → 11001 and (2) η: 0 → 001,1 → 11100. We show that the substitution subshifts arising from θand ηhave minimal self-joinings and are mildly mixing. We also give a criterion for 1-dimensional tiling systems arising from θor ηto have minimal self-joinings. We apply this to obtain examples of mildly mixing 1-dimensional tiling systems.

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• Special flow systems with the minimal self-joining property

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