Quadratic systems with invariant straight lines of total multiplicity two having Darboux invariants

DOI10.1142/S0219199714500187zbMath1319.34052OpenAlexW2110548685MaRDI QIDQ4983010

Jaume Llibre, Regilene D. S. Oliveira

Publication date: 14 April 2015

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199714500187

zbMATH Keywords

phase portraitsquadratic vector fieldsDarboux invariants

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Invariant manifolds for ordinary differential equations (34C45)

Related Items (9)

Quadratic systems with an invariant conic having Darboux invariants ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Unnamed Item ⋮ Nonchaotic Behavior in Quadratic Three-Dimensional Differential Systems with a Symmetric Jacobian Matrix ⋮ Polynomial differential systems in \(\mathbb R^3\) having invariant weighted homogeneous surfaces ⋮ Darboux invariants for planar polynomial differential systems having an invariant conic ⋮ Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces ⋮ Final evolutions of a class of May-Leonard Lotka-Volterra systems ⋮ Integrability and Dynamics of Quadratic Three-Dimensional Differential Systems Having an Invariant Paraboloid

Cites Work

• Chordal quadratic systems
• Classification and Analysis of two-dimensional real homogeneous quadratic differential equation systems
• Darbouxian first integrals and invariants for real quadratic systems having an invariant conic

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