Small divisor problem in dynamical systems and analytic solutions of a \(q\)-difference equation with a singularity at the origin
type: Item
instance of: scholarly article
title: Small divisor problem in dynamical systems and analytic solutions of a \(q\)-difference equation with a singularity at the origin
zbMATH Open document ID: 1210.39005
author: Hou Yu Zhao
author: Jianguo Si
published in: Results in Mathematics
publication date: 2010-11-17T00:00:00Z
review text: The authors consider the existence of locally analytic solutions of the \(q\)-difference equation \[ \sum_{j=0}^k \sum_{t=1}^\infty C_{t,j}(z)\,\big( y(q^jz) \big)^t =G(z) \] in \({\mathbb C}\), where \(z=0\) is a pole of the functions \(C_{t,j}(z)\) for \(t\in{\mathbb N}\), \(j\in\{0,1,\dots,k\}\), with order \(h_1\) and a pole of \(G(z)\) with order \(h_2\).
reviewed by: Roman Šimon Hilscher
Mathematics Subject Classification ID: 39A13
zbMATH DE Number: 5816641
zbMATH Keywords: \(q\)-difference equation
zbMATH Keywords: analytic solution
zbMATH Keywords: small divisor
zbMATH Keywords: Diophantine condition
zbMATH Keywords: Brjuno condition
MaRDI profile type: Publication
full work available at URL: s00025-010-0060-2
OpenAlex ID: W1992318837
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DOI: 10.1007/S00025-010-0060-2
description: scientific article; zbMATH DE number 5816641