A Galoisian proof of Ritt theorem on the differential transcendence of Poincar\'e functions - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

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

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 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.

Dates and versions

hal-03146286 , version 1 (18-02-2021)

Identifiers

Cite

Lucia Di Vizio, Gwladys Fernandes. A Galoisian proof of Ritt theorem on the differential transcendence of Poincar\'e functions. 2021. ⟨hal-03146286⟩
32 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More