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Quaestiones Mathematicae

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Symmetric intersections of Rauzy fractals

Tarek Sellami, Víctor F. Sirvent

Abstract


In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is symmetric and it is obtained by the balanced pair algorithm associated with both substitutions.

Keywords: Rauzy fractals, substitution dynamical systems, balanced pair algorithm, symmetry groups, Pisot conjecture




http://dx.doi.org/10.2989/16073606.2015.1073189
AJOL African Journals Online