Analytic invariant curves for a planar mapping
type: Item
instance of: scholarly article
title: Analytic invariant curves for a planar mapping
zbMATH Open document ID: 1151.39018
author: Han-Ze Liu
author: Li Yin
author: Wenrong Li
publication date: 2008-09-09T00:00:00Z
review text: The main object of this paper is the investigation of the single variable functional equation \[ f[p(z)+q(f(z))]=h(f(z)), \qquad z\in\mathbb{C}, \] where \(p,q\), and \(h\) are given analytic functions. This equation characterizes the invariance of the curve \(w=f(z)\) under the planar mapping \(T(w,z)=(p(z)+q(w),h(w))\). By constructing a convergent power series solution of an auxiliary functional equation, the existence of analytic solutions in a neighborhood of zero of the above equation is proved.
reviewed by: Zsolt Páles
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 30D05
zbMATH DE Number: 5323408
zbMATH Keywords: planar mapping
zbMATH Keywords: invariant curve
zbMATH Keywords: analytic solution
zbMATH Keywords: majorant series
zbMATH Keywords: functional equation
zbMATH Keywords: power series solution
MaRDI profile type: Publication
full work available at URL: s10114-007-6221-x
OpenAlex ID: W2064278306
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DOI: 10.1007/S10114-007-6221-X
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5323408