Journal of Statistical Physics, Vol. 34, Nos. 1/2, 1984, p. 57-73.
The investigation of a scaling limit for mappings of the circle to itself with
golden ratio rotation number leads to a pair of functional equations with at least
a formal resemblance to the functional equation using the accumulation of
period-doubling bifurcations. We discuss the general theory of these functional
equations, assuming that solutions exist.