Integrability and Dynamics of Quadratic Three-Dimensional Differential Systems Having an Invariant Paraboloid

DOI10.1142/S0218127416501340zbMath1345.34017MaRDI QIDQ2819426

Marcelo Messias, Alisson C. Reinol

Publication date: 29 September 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

polynomial differential systemshomoclinic and heteroclinic orbitsRabinovich systeminvariant algebraic surfacesPoincaré compactificationDarboux theory of integrabilityelliptic paraboloidinvariant parallels and meridians

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Equivalence and asymptotic equivalence of ordinary differential equations (34C41)

Related Items (5)

Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine ⋮ Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations ⋮ 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 ⋮ Normal forms of polynomial differential systems in \(\mathbb{R}^3\) having at least three invariant algebraic surfaces

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