An Ergodic Adding Machine on the Cantor Set

We calculate all ergodic measures for a specific function F on the unit interval. The supports of these measures consist of periodic orbits of period 2n and the classical ternary Cantor set. On the Cantor set, F is topologically conjugate to an “adding machine” in base 2. We show that F is representative of the class of functions with zero topological entropy on the unit interval, already analyzed in the literature, and its behavior is therefore typical of that class.