Algorithms for formal reduction of vector field singularities
type: Item
instance of: scholarly article
title: Algorithms for formal reduction of vector field singularities
zbMATH Open document ID: 1029.34029
DOI: 10.1023/A:1026601823458
author: Yanyan Li
published in: Journal of Dynamical and Control Systems
publication date: 2003-04-27T00:00:00Z
review text: The authors present several algorithms transforming a Pfaffian form of the type \(\omega = d(y^2 - x^q) + \delta(x, y) (2x +dy - qydx)\) into the normal form given by \textit{F. Loray} [J. Differ. Equations 158, 152-173 (1999; Zbl 0985.37014)] in the cases \(q = 2\) and \(q =3\). The main results give a numerical answer to the question on the convergence of normal forms. For \( q =3\), in the nondegenerate case, their numerical analysis of algorithms leads to Gevrey estimates of order 2. Moreover, in the case \(q =2\), their results agree with the results of \textit{J. Martinet} and \textit{J.-P. Ramis} [Ann. Sci. Éc. Norm. Supér. 16, 571-621 (1983; Zbl 0534.34011)].
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37G05
Mathematics Subject Classification ID: 37M20
Mathematics Subject Classification ID: 58K45
zbMATH DE Number: 1901425
zbMATH Keywords: normal forms
zbMATH Keywords: Gevrey theory
zbMATH Keywords: formal power series
zbMATH Keywords: symbolic computation
reviewed by: Yuefei Wang
MaRDI profile type: Publication
full work available at URL: a:1026601823458
OpenAlex ID: W1565074327
description: scientific article; zbMATH DE number 1901425