Linear recursion formulas of quantities of singular point and applications.
type: Item
instance of: scholarly article
title: Linear recursion formulas of quantities of singular point and applications.
zbMATH Open document ID: 1053.65051
DOI: 10.1016/S0096-3003(02)00835-4
author: Haibo Chen
author: Yirong Liu
published in: Applied Mathematics and Computation
publication date: 2003-12-03T00:00:00Z
review text: The authors investigate real planar ordinary differential equations in the vicinity of singular points whose linear normal form is a center. With the use of a change of variables the system can be reduced to a normal form represented by formal power series. Based on that form the authors derive quantities which allow in principle a description of the dynamics. Moreover, recursion formulae for these quatities are proveded. Thus, the calculation can be done with computer algebra systems such as Mathematica. For polynomial planar systems up to cubic terms a complete explicit representation of these quantities is given. Finally, this process is illustrated by discussing an example.
reviewed by: Johannes Schropp
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 2012686
zbMATH Keywords: planar autonomous systems
zbMATH Keywords: singular point
zbMATH Keywords: normal form
zbMATH Keywords: numerical example
zbMATH Keywords: computer algebra systems
describes a project that uses: Mathematica
MaRDI profile type: Publication
cites work: Saddle quantities and applications
cites work: An explicit expression of the first Lyapunov and period constants with applications
cites work: Ljapunov approach to multiple Hopf bifurcation
cites work: Q4715040
full work available at URL: s0096-3003(02)00835-4
OpenAlex ID: W2091738011
description: scientific article; zbMATH DE number 2012686