Abstract

Two Rauzy fractals are congruent if they differ by an affine transformation only. We give conditions on unimodular Pisot substitutions in order to ensure the congruence of the Rauzy fractals. We use these results to characterise a large family of substitutions that yield central symmetric Rauzy fractals in terms of the induced language. (C) 2016 Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG).