Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in \(\mathbb R^3\)

DOI10.1007/s10884-013-9315-4zbMath1300.34103OpenAlexW2012945942MaRDI QIDQ376302

Jaume Llibre, Salomón Rebollo-Perdomo

Publication date: 4 November 2013

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-013-9315-4

zbMATH Keywords

limit cycleinvariant toruspolynomial vector fieldinvariant meridianinvariant parallel

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Dynamics induced by flows and semiflows (37C10) Invariant manifolds for ordinary differential equations (34C45) Ordinary differential equations and systems on manifolds (34C40)

Related Items (7)

Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine ⋮ Polynomial vector fields on algebraic surfaces of revolution ⋮ On the number of invariant conics for the polynomial vector fields defined on quadrics ⋮ Invariant hyperplane sections of vector fields on the product of spheres ⋮ Integrability and Dynamics of Quadratic Three-Dimensional Differential Systems Having an Invariant Paraboloid ⋮ When Parallels and Meridians are Limit Cycles for Polynomial Vector Fields on Quadrics of Revolution in the Euclidean 3-Space ⋮ Polynomial Vector Fields on the Clifford Torus

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