# 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.

## References

SHOWING 1-10 OF 11 REFERENCES

σ -Galois Theory of Linear Difference Equations

- Mathematics
- 2015

Inspired by the numerous applications of the differential algebraic independence results from [36], we develop a Galois theory with an action of an endomorphism σ for systems of linear difference…

Periodic functions with a multiplication theorem

- Mathematics
- 1922

Let /(z) represent a uniform analytic function with no essential singularity in the finite part of the plane, and periodic, either simply or doubly. There exists in certain cases a number ra,…

Enveloppe galoisienne d'une application rationnelle de P1

- Geology
- 2005

Galoisian envelope of a rational map. lo 2001, a. Maigrange defines Ibe 21-envelope or galoisian envelope of an analytical dynamical system. Roughly speakiog, tbis is the algebrair boil of the…

A Survey on the Hypertranscendence of the Solutions of the Schröder’s, Böttcher’s and Abel’s Equations

- MathematicsTranscendence in Algebra, Combinatorics, Geometry and Number Theory
- 2021

In 1994, P.-G. Becker and W. Bergweiler [8] listed all the differentially algebraic solutions of three famous functional equations: the Schröder’s, Böttcher’s and Abel’s equations. The proof of this…

A survey on the hypertranscendence of the solutions of the Schröder’s, Böttcher’s and Abel’s equations, Proceedings of the conference “Transient Transcendence in Transylvania

- Proceedings in Mathematics & Statistics,
- 2021

Difference Galois Theory for the “Applied” Mathematician

- Mathematics
- 2020

The lecture notes below correspond to the course given by the author in occasion of the VIASM school on Number Theory (18–24 June 2018, Hanoi). We have chosen to omit the proofs that are already…

El grupoide de galois de una transformacin racional

- VIII Escuela Doctoral intercontinental de Matematicas PUCP
- 2015

Springer-Verlag

- Berlin,
- 1997