  We 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.
