• Corpus ID: 231934218

A Galoisian proof of Ritt theorem on the differential transcendence of Poincar\'e functions

@inproceedings{Vizio2021AGP,
  title={A Galoisian proof of Ritt theorem on the differential transcendence of Poincar\'e functions},
  author={Lucia Di Vizio and Gwladys Fernandes},
  year={2021}
}
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) ∈ C(t) verifies R(0) = 0, R′(0) = q ∈ C, with |q| > 1. We also give a partial result in the case of an algebraic function R. 2010 Mathematics Subject Classification: 30D05, 34M15, 39B12. 
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COHERENT FAMILIES OF POLYNOMIALS
Transcendental transcendency of certain functions of Poincaré
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