Poincaré函数微分超越Ritt定理的Galois证明
A Galoisian proof of Ritt theorem on the differential transcendence of Poincaré functions
摘要：
利用函数方程的伽罗瓦论，对J.F. Ritt，关于函数方程R（y（t））=y（qt）的解的微分超越，其中R是复系数有理函数，证明R（0）=0，R '（0）=q，其中q是|q| >1的复数.在代数函数R的情况下，我们也给出了一个部分结果。
英文摘要：
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 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.
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