with Gwladys Fernandes

#### Abstract:

Using Galois theory of functional equations, we give a new proof of the main result of the paper "Transcendental transcendency of certain functions of Poincaré'' by J.F.~Ritt, on the differential transcendence of the solutions of the functional equation \(R(y(t))=y(qt)\), where \(R(t)\in\mathbb C(t)\) verifies \(R(0)=0\), \(R'(0)=q\in\mathbb C\), with \(|q|>1\).

We also give a partial result in the case of an algebraic function \(R\).

DOI:

ArXiv: 2102.08268

HAL: hal-03146286