Classical Planar Algebraic Curves Realizable by Quadratic Polynomial Differential Systems

DOI10.1142/S0218127417501413zbMath1373.34048OpenAlexW2692842713MaRDI QIDQ5371178

Jaume Llibre, Isaac A. García

Publication date: 25 October 2017

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127417501413

zbMATH Keywords

Darboux integrabilityinvariant algebraic curvequadratic differential system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05) Invariant manifolds for ordinary differential equations (34C45)

Related Items

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Number of limit cycles for planar systems with invariant algebraic curves ⋮ Global phase portraits of quadratic polynomial differential systems having as solution some classical planar algebraic curves of degree 6

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A survey on the inverse integrating factor
• Equations de Pfaff algébriques
• Configurations of limit cycles and planar polynomial vector fields.
• Mathematical problems for the next century
• Hilbert's problems and their sequels
• Qualitative theory of planar differential systems
• A survey of quadratic systems
• Elementary First Integrals of Differential Equations
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• On General Properties of Quadratic Systems
• Liouvillian First Integrals of Differential Equations
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS