Algebraic and topological classification of homogeneous quartic vector fields in the plane
type: Item
instance of: scholarly article
title: Algebraic and topological classification of homogeneous quartic vector fields in the plane
zbMATH Open document ID: 1497.37029
author: Jaume Llibre
author: Y. P. Martínez
author: Claudio Vidal
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2022-03-22T00:00:00Z
review text: The authors consider the problem of the algebraic and topological classification of the following planar homogeneous quartic system: \[ \dot{x}=P(x, y),\quad \dot{y}=Q(x, y), \] where \(P\) and \(Q\) are homogeneous polynomials of degree four. They first provide all of the possible canonical forms of homogeneous polynomials of degree five. Then they present all the possible phase portraits in the Poincaré disk of the above quartic system. They prove that the system has exactly 23 different topological phase portraits.
reviewed by: Zhengdong Du
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
zbMATH DE Number: 7495326
zbMATH Keywords: quartic homogeneous polynomial differential systems
zbMATH Keywords: homogeneous polynomial vector fields
zbMATH Keywords: phase portraits
MaRDI profile type: Publication
full work available at URL: s10231-021-01106-5
OpenAlex ID: W3156015756
cites work: Sur les points singuliers multiples de systèmes dynamiques dans \(R^ 2\)
cites work: On polynomial Hamiltonian planar vector fields
cites work: Algebraic and topological classification of the homogeneous cubic vector fields in the plane
cites work: Algebraic classification of homogeneous polynomial vector fields in the plane
cites work: Cofactors and equilibria for polynomial vector fields
cites work: Canonical forms of real homogeneous quadratic transformations
cites work: Qualitative theory of planar differential systems
cites work: Generic Properties of Polynomial Vector Fields at Infinity
cites work: Q5336331
cites work: Q5731038
cites work: Global Structure of Ordinary Differential Equations in the Plane
cites work: Classification of Continuous Flows on 2-Manifolds
cites work: Q3715459
DOI: 10.1007/S10231-021-01106-5
description: scientific article; zbMATH DE number 7495326