Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space \(\mathbb R^{12}\)
type: Item
instance of: scholarly article
title: Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space \(\mathbb R^{12}\)
zbMATH Open document ID: 1213.34004
author: Joan C. Artés
author: Jaume Llibre
author: Nicolae Vulpe
publication date: 2011-01-25T00:00:00Z
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 5841042
zbMATH Keywords: quadratic vector fields
zbMATH Keywords: integrability
zbMATH Keywords: rational first integral
zbMATH Keywords: phase portraits
zbMATH Keywords: invariants
MaRDI profile type: Publication
full work available at URL: s12215-010-0032-0
OpenAlex ID: W2015308657
cites work: Quadratic system with a rational first integral of degree 2: a complete classification in the coefficient space \(\mathbb{R}^{12}\)
cites work: SINGULAR POINTS OF QUADRATIC SYSTEMS: A COMPLETE CLASSIFICATION IN THE COEFFICIENT SPACE ℝ12
cites work: Quadratic systems with a polynomial first integral: A complete classification in the coefficient space \(\mathbb R^{12}\)
cites work: Q4812876
cites work: Total multiplicity of all finite critical points of the polynomial differential system
cites work: Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2
cites work: Q4812881
cites work: Polynomial first integrals of quadratic vector fields
cites work: Phase portaits of the quadratic vector fields with a polynominal first integral
cites work: Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3
cites work: Erratum to ``Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3'' [Nonlinear Anal. 70 (2009) 3549-3560]
cites work: Phase portraits for quadratic homogeneous polynomial vector fields on \(\mathbb S^{2}\)
cites work: Q4509277
cites work: Sur ĽintÉgration algÉbrique des Équations diffÉrentielles du premier ordre et du premier degrÉ
cites work: Planar quadratic vector fields with invariant lines of total multiplicity at least five
cites work: Geometry of quadratic differential systems in the neighborhood of infinity
cites work: Integrals and phase portraits of planar quadratic differential systems with invariant lines of at least five total multiplicity
cites work: Planar quadratic differential systems with invariant straight lines of total multiplicity four
cites work: The full study of planar quadratic differential systems possessing a line of singularities at infinity
cites work: Q3542504
cites work: Q3220899
cites work: Q4400966
DOI: 10.1007/S12215-010-0032-0
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 5841042