First integrals and phase portraits of planar polynomial differential cubic systems with the maximum number of invariant straight lines

DOI10.1007/s12346-016-0211-2zbMath1367.34030OpenAlexW2510480637MaRDI QIDQ2628038

Cristina Bujac, Nicolae Vulpe, Jaume Llibre

Publication date: 9 June 2017

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/169492

zbMATH Keywords

cubic systemfirst integralphase portraitinvariant straight lines

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 (5)

Unnamed Item ⋮ Unnamed Item ⋮ Dynamics of the cubic Darboux systems ⋮ Unnamed Item ⋮ Limit cycle bifurcations from a quadratic center with two switching lines

Cites Work

• Cubic differential systems with invariant straight lines of total multiplicity eight and four distinct infinite singularities
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• Total multiplicity of all finite critical points of the polynomial differential system
• Cubic systems with invariant straight lines of total multiplicity eight and with three distinct infinite singularities
• Planar quadratic vector fields with invariant lines of total multiplicity at least five
• Darboux theory of integrability in \(\mathbb C^n\) taking into account the multiplicity
• Planar quadratic differential systems with invariant straight lines of total multiplicity four
• Planar cubic polynomial differential systems with the maximum number of invariant straight lines
• Qualitative theory of planar differential systems
• Classification of cubic differential systems with invariant straight lines of total multiplicity eight and two distinct infinite singularities
• On the number of invariant lines for polynomial vector fields
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