  Using Galois theory of functional equations, we give a new proof of the main
result of the paper "Transcendental transcendency of certain functions of
Poincar\'e" by J.F. Ritt, on the differential transcendence of the solutions of
the functional equation R(y(t))=y(qt), where R is a rational function with
complex coefficients which verifies R(0)=0, R'(0)=q, where q is a complex
number with |q|>1. We also give a partial result in the case of an algebraic
function R.
