Integrable third-order mappings and their growth properties
type: Item
instance of: scholarly article
title: Integrable third-order mappings and their growth properties
zbMATH Open document ID: 1011.39017
author: Stéphane Lafortune
author: A. S. Carstea
author: A. Ramani
author: B. Grammaticos
author: Yasuhiro Ohta
published in: Regular and Chaotic Dynamics
publication date: 2003-02-24T00:00:00Z
review text: The authors study the degree growth of the iterates of the initial conditions for a class of third-order integrable mappings which result from the coupling of a discrete Painlevé equation to a homographic method. They show that the degree grows like \(n^3\). In the special cases where the mapping satisfies a singularity confinement requirement they find a slower, quadratic growth. Finally they present a method for the construction of integrable \(N\)th-order mappings with degree growth \(n^N\).
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 37J35
zbMATH DE Number: 1873384
zbMATH Keywords: difference equation
zbMATH Keywords: discrete Painlevé equation
zbMATH Keywords: integrable discrete system
reviewed by: I. A. Taimanov
MaRDI profile type: Publication
DOI: 10.1070/RD2001V006N04ABEH000188
description: scientific article; zbMATH DE number 1873384