Hilbert space description of nonlinear discrete-time dynamical systems
type: Item
instance of: scholarly article
title: Hilbert space description of nonlinear discrete-time dynamical systems
zbMATH Open document ID: 0811.58053
DOI: 10.1016/0378-4371(93)90258-6
author: Krzysztof Kowalski
published in: Physica A
publication date: 1995-05-03T00:00:00Z
review text: The author shows that very general nonlinear recurrences of the form \(x_{n + 1} = f(x_ n)\) where \(f\) is analytic in \(x_ n\) may be cast into the linear abstract recurrence in Hilbert space with the displacement operator expressed in terms of Bose creation and annihilation operators. This generalizes the Carleman linearization approach that corresponds to the particular occupation number representation [see the author and \textit{W.-H. Steeb}, `Nonlinear dynamical systems and Carleman linearization' (1991; Zbl 0753.34003) and \textit{W.-H. Steeb}, in `Nonlinear phenomena in chemical dynamics' (1991)]. The formalism introduced in the paper is applied to the study of the linearization transformations for nonlinear difference equations and Feigenbaum-Cvitanovic renormalization equations.
Mathematics Subject Classification ID: 37F99
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 606944
zbMATH Keywords: nonlinear recurrences
zbMATH Keywords: Bose creation
zbMATH Keywords: annihilation operators
zbMATH Keywords: Feigenbaum- Cvitanovic renormalization equations
reviewed by: Abdul-Aziz Yakubu
MaRDI profile type: Publication
full work available at URL: 0378-4371(93)90258-6
OpenAlex ID: W1976505484
cites work: Hilbert space description of classical dynamical systems. I
cites work: Hilbert space description of classical dynamical systems. II
cites work: Q4002304
cites work: Q3696187
description: scientific article; zbMATH DE number 606944