An algorithm for computing a new normal form for dynamical systems
type: Item
instance of: scholarly article
title: An algorithm for computing a new normal form for dynamical systems
zbMATH Open document ID: 0973.34029
author: Guoting Chen
author: Jean Della Dora
published in: Journal of Symbolic Computation
publication date: 2001-11-27T00:00:00Z
review text: Autonomous dynamical systems \(\dot{x}=F(x)\) are considered, with \(x\in \mathbb{R}^n\), \(F(x)\) is a vector whose components are formal power series and \(F(0)=0\). A new formal normal form for system (1) is proposed which improves the classical normal forms in the sense that it is a further reduction of the classical normal forms. An algorithm for an effective computation of these normal forms is given. All computations are done in a field \(K\), if the coefficients of the system are in \(K\). As a particular case, if the matrix of the linear part is a companion matrix then the dynamical system can be reduced to a single differential equation. The method is applicable for both the nilpotent and the nonnilpotent cases. The algorithm is implemented in MAPLE V and many examples of the further reduced normal forms up to some finite order are obtained.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 58K50
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 37G05
zbMATH DE Number: 1445834
zbMATH Keywords: perturbation
zbMATH Keywords: formal normal form
zbMATH Keywords: vector field
zbMATH Keywords: dynamical system
describes a project that uses: Maple
MaRDI profile type: Publication
OpenAlex ID: W2063943049
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DOI: 10.1006/JSCO.1999.0305
description: scientific article; zbMATH DE number 1445834