Cubic differential systems with invariant straight lines of total multiplicity eight and four distinct infinite singularities

DOI10.1016/j.jmaa.2014.10.014zbMath1312.34070OpenAlexW2010557778MaRDI QIDQ472312

Nicolae Vulpe, Cristina Bujac

Publication date: 19 November 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.10.014

zbMATH Keywords

singular pointgroup actioncubic differential systemaffine invariant polynomialconfiguration of invariant linesinvariant line

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) Invariant manifolds for ordinary differential equations (34C45)

Related Items (7)

First integrals and phase portraits of planar polynomial differential cubic systems with the maximum number of invariant straight lines ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Cubic differential systems with invariant straight lines of total multiplicity eight possessing one infinite singularity ⋮ Unnamed Item ⋮ Cubic systems with invariant straight lines of total multiplicity eight and with three distinct infinite singularities

Cites Work

• Global classification of the planar Lotka-Volterra differential systems according to their configurations of invariant straight lines
• Multiplicity of invariant algebraic curves in polynomial vector fields
• Integrals and phase portraits of planar quadratic differential systems with invariant lines of at least five total multiplicity
• On the invariant straight lines of polynomial differential systems
• Planar quadratic vector fields with invariant lines of total multiplicity at least five
• 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
• On the number of invariant lines for polynomial vector fields
• Cubic systems with four real line invariants
• Erratum: Bigradients and the Problem of Routh and Hurwitz
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