2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125952We study the dynamics of renormalisation of an interval exchange transformation which features exact scaling (the cubic Arnoux-Yoccoz model). Using a symbolic space that describes both dynamics and scaling, we characterize the periodic points of the scaling map in terms of generalised decimal expansions, where the base is the reciprocal of a Pisot number and the digits are algebraic integers. We establish rigorously some basic facts, and use extensive numerical experimentation to formulate a conjecture.18 pagesDynamical SystemsNumber Theory37E05; 11Z05; 37E20text