Algebraic solutions of plane vector fields
type: Item
instance of: scholarly article
title: Algebraic solutions of plane vector fields
zbMATH Open document ID: 1155.37035
author: S. C. Coutinho
author: L. Menasché Schechter
published in: Journal of Pure and Applied Algebra
publication date: 2008-11-11T00:00:00Z
review text: The presence of an algebraic curve invariant under a vector field allows to find a first integral of the corresponding differential equation. Invariant curves are also important in the study of centres of planar systems of differential equations. The authors present an algorithm which checks whether a given derivation of the complex affine plane has an invariant algebraic curve. They discuss the performance of its implementation in the computer system SINGULAR.
Mathematics Subject Classification ID: 37F75
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 34M45
zbMATH DE Number: 5364863
zbMATH Keywords: invariant algebraic curve
zbMATH Keywords: derivation
zbMATH Keywords: vector field
reviewed by: Vladimir P. Kostov
describes a project that uses: SINGULAR
MaRDI profile type: Publication
full work available at URL: j.jpaa.2008.06.003
OpenAlex ID: W2007467867
cites work: On non-holonomic irreducible \(D\)-modules
cites work: Q4663519
cites work: Invariant varieties through singularities of holomorphic vector fields
cites work: Holomorphic foliations in \(CP(2)\) having an invariant algebraic curve
cites work: Invariant algebraic curves and conditions for a centre
cites work: Limit cycles of differential equations
cites work: Multiplicity of invariant algebraic curves in polynomial vector fields
cites work: INDECOMPOSABLE NON-HOLONOMIC $\mathcal{D}$-MODULES IN DIMENSION $2$
cites work: Algebraic solutions of holomorphic foliations: an algorithmic approach
cites work: Q5571530
cites work: Q5843703
cites work: Equations de Pfaff algébriques
cites work: Q4507801
cites work: Q5694787
cites work: On the number of limit cycles of the equation \frac{𝑑𝑦}𝑑𝑥=\frac{𝑃(𝑥,𝑦)}𝑄(𝑥,𝑦)’ where 𝑃 and 𝑄 are polynomials of the second degree
cites work: A rational approach to the Prelle-Singer algorithm
cites work: On topological rigidity of projective foliations
cites work: Vector fields, invariant varieties and linear systems.
cites work: Elementary First Integrals of Differential Equations
cites work: Q3843136
cites work: On the Poincaré problem
DOI: 10.1016/J.JPAA.2008.06.003
description: scientific article; zbMATH DE number 5364863