Phase portraits for quadratic homogeneous polynomial vector fields on \(\mathbb S^{2}\)

DOI10.1007/s12215-009-0030-2zbMath1196.34040arXiv0810.2754OpenAlexW1619769442MaRDI QIDQ2269948

Claudio Pessoa, Jaume Llibre

Publication date: 12 March 2010

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

Full work available at URL: https://arxiv.org/abs/0810.2754

zbMATH Keywords

limit cyclescenterspolynomial vector fieldinvariant algebraic curves

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (6)

Quadratic systems with a rational first integral of degree three: a complete classification in the coefficient space \(\mathbb R^{12}\) ⋮ Invariant circles and phase portraits of cubic vector fields on the sphere ⋮ On the reversible quadratic polynomial vector fields on \(\mathbb{S}^2\) ⋮ A class of reversible quadratic polynomial vector fields on \(\mathbb S^2\) ⋮ Planar semi-quasi homogeneous polynomial differential systems with a given degree ⋮ Global phase portraits and bifurcation diagrams for reversible equivariant Hamiltonian systems of linear plus quartic homogeneous polynomials

Cites Work

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• Global topological properties of homogeneous vector fields in \(R^3\)
• Limit cycles of a planar vector field
• Limit-cycles and rotated vector fields
• Geometric Properties of Homogeneous Vector Fields of Degree Two in R 3
• On the nonexistence, existence and uniqueness of limit cycles
• Invariant algebraic curves and rational first integrals for planar polynomial vector fields
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