Sur les équation fonctionelles aux itérées. (On iterated functional equations)
type: Item
instance of: scholarly article
title: Sur les équation fonctionelles aux itérées. (On iterated functional equations)
zbMATH Open document ID: 0697.39008
DOI: 10.1007/BF01833943
author: J.-P. Bézivin
published in: Aequationes Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137338
review text: The author studies solutions of functional equations \(P(f^ 0,...,f^ s)=0\), where P is a non-zero polynomial is \(s+1\) variables and \(f^ k\) denotes the k-th iterate of the function f. It is proved that, if f is either an entire function of a complex variable or an entire function of a p-adic variable, then f is a polynomial. Moreover, it is shown that, if f is a formal power series with coefficients in a number field \({\mathbb{K}}\), then subject to some natural restrictions on f and on P f is an algebraic power series over the ring of polynomials in \(Kx\).
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 4142693
zbMATH Keywords: p-adic analytic function
zbMATH Keywords: entire function
zbMATH Keywords: formal power series
zbMATH Keywords: number field
reviewed by: Marek Cezary Zdun
MaRDI profile type: Publication
cites work: Kleene computable functionals and the higher order existence property
cites work: Linear Independence of Iterates and Entire Solutions of Functional Equations
cites work: Q5723337
cites work: Primitive divisors of the expression An - Bn in algebraic number fields.
cites work: Iteration of analytic functions
description: scientific article; zbMATH DE number 4142693