Phase portraits and invariant straight lines of cubic polynomial vector fields having a quadratic rational first integral

DOI10.1216/RMJ-2011-41-5-1585zbMath1232.34006MaRDI QIDQ640275

Adam Mahdi, Jaume Llibre, Nicolae Vulpe

Publication date: 18 October 2011

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

integrabilityquadratic vector fieldphase portraitrational first integral

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (4)

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2 ⋮ Detection of special curves via the double resultant ⋮ Limit cycles for a class of continuous and discontinuous cubic polynomial differential systems ⋮ On the topological equivalence of flows of Brouwer homeomorphisms

Cites Work

• Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2
• Multiplicity of invariant algebraic curves in polynomial vector fields
• Quadratic system with a rational first integral of degree 2: a complete classification in the coefficient space \(\mathbb{R}^{12}\)
• Planar cubic polynomial differential systems with the maximum number of invariant straight lines
• Qualitative theory of planar differential systems
• Phase portraits of cubic polynomial vector fields of Lotka–Volterra type having a rational first integral of degree 2
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