Planar cubic polynomial differential systems with the maximum number of invariant straight lines

DOI10.1216/rmjm/1181069417zbMath1139.34035arXivmath/0404531OpenAlexW2075400176MaRDI QIDQ2477889

Nicolae Vulpe, Jaume Llibre

Publication date: 14 March 2008

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

Full work available at URL: https://arxiv.org/abs/math/0404531

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Dynamics induced by flows and semiflows (37C10)

Related Items (13)

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 ⋮ Normal forms of planar polynomial differential systems ⋮ Cubic differential systems with invariant straight lines of total multiplicity eight possessing one infinite singularity ⋮ Phase portraits and invariant straight lines of cubic polynomial vector fields having a quadratic rational first integral ⋮ Cubic differential systems with invariant straight lines of total multiplicity eight and four distinct infinite singularities ⋮ Unnamed Item ⋮ On invariant line arrangements ⋮ Unnamed Item ⋮ Cubic systems with invariant straight lines of total multiplicity eight and with three distinct infinite singularities ⋮ Classification of a class of systems of cubic ordinary differential equations

Cites Work

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• Multiplicity of invariant algebraic curves in polynomial vector fields
• On the number of invariant straight lines for polynomial differential systems
• Planar quadratic vector fields with invariant lines of total multiplicity at least five
• Geometry of quadratic differential systems in the neighborhood of infinity
• On the number of invariant lines for polynomial vector fields
• Bigradients and the Problem of Routh and Hurwitz

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