Elementary first integrals and algebraic invariant curves of differential equations
type: Item
instance of: scholarly article
title: Elementary first integrals and algebraic invariant curves of differential equations
zbMATH Open document ID: 0791.34004
author: Dana Schlomiuk
published in: Expositiones Mathematicae
publication date: 1994-07-11T00:00:00Z
review text: From author's summary: ``In this work we survey the relationship existing between existence of elementary first integrals of differential equations and invariant algebraic curves. We explain the method of integration of polynomial differential equations via invariant algebraic curves, method introduced by Darboux and developed later by Prelle and Singer. We indicate the importance of this method for the problem of the center for plane polynomial vector fields. We illustrate the method by exhibiting a simple and unifying proof of both the sufficiency of the algebraic conditions for the center and of the integrability of systems satisfying them in the case of quadratic systems, for all values of the parameters. Other applications and some open problems are mentioned''.
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34-02
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 495531
zbMATH Keywords: survey
zbMATH Keywords: existence of elementary first integrals
zbMATH Keywords: invariant algebraic curves
zbMATH Keywords: method of integration of polynomial differential equations
zbMATH Keywords: problem of the center
zbMATH Keywords: integrability
reviewed by: Sergei A. Mazanik
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 495531