Invariant circles for homogeneous polynomial vector fields on the 2-dimensional sphere

DOI10.1007/BF02874668zbMath1150.37003OpenAlexW2088783027MaRDI QIDQ997521

Jaume Llibre, Claudio Pessoa

Publication date: 7 August 2007

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02874668

zbMATH Keywords

polynomial vector fieldinvariant circlesinvariant great circles

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10)

Related Items (13)

Quadratic three-dimensional differential systems having invariant planes with total multiplicity nine ⋮ Polynomial vector fields on algebraic surfaces of revolution ⋮ Invariant parallels, invariant meridians and limit cycles of polynomial vector fields on some 2-dimensional algebraic tori in \(\mathbb R^3\) ⋮ Limit cycles, invariant meridians and parallels for polynomial vector fields on the torus ⋮ Invariant circles and phase portraits of cubic vector fields on the sphere ⋮ Extended quasi-homogeneous polynomial system in \({\mathbb{R}^{3}}\) ⋮ Centers and limit cycles of vector fields defined on invariant spheres ⋮ The projective vector field of a kind of three-dimensional quasi-homogeneous system on \(\mathbb S\) ⋮ Phase portraits for quadratic homogeneous polynomial vector fields on \(\mathbb S^{2}\) ⋮ On the reversible quadratic polynomial vector fields on \(\mathbb{S}^2\) ⋮ A class of reversible quadratic polynomial vector fields on \(\mathbb S^2\) ⋮ 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

Cites Work

• On the number of invariant straight lines for polynomial differential systems
• Invariant hyperplanes and Darboux integrability for \(d\)-dimensional polynomial differential systems
• Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces
• Geometric Properties of Homogeneous Vector Fields of Degree Two in R 3
• Integrable systems in the plane with center type linear part
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