A Galoisian proof of Ritt theorem on the differential transcendence of Poincaré functions

16 Feb 2021  ·  Lucia Di Vizio, Gwladys Fernandes ·

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. read more

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Dynamical Systems Classical Analysis and ODEs Complex Variables 30D05, 34M15, 39B12