Balanced pair algorithm for a class of cubic substitutions

Authors: TAREK SELLAMI

Abstract: In this article we introduce the balanced pair algorithm associated with 2 unimodular Pisot substitutions having the same incidence matrix. We are interested in beta-substitution related to the polynomial x^3 - ax^2 - bx-1 for a \geq b \geq 1. Applying the balanced pair algorithm to these substitutions, we obtain a general formula for the associated intersection substitution.

Keywords: Rauzy fractals, substitution dynamical systems, balanced pair algorithm The author was supported by project I 11 36 funded by the Austrian Science Fund

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