Limit cycles for cubic systems with a symmetry of order 4 and without infinite critical points

DOI10.1090/S0002-9939-07-09072-7zbMath1142.34017OpenAlexW1980998968MaRDI QIDQ5438477

Rafel Prohens, Maria Jesus Alvarez, Armengol Gasull

Publication date: 23 January 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-07-09072-7

zbMATH Keywords

limit cycleAbel equationHilbert's 16th problemplanar autonomous ordinary differential equationssymmetric cubic system

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) 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) Periodic orbits of vector fields and flows (37C27)

Related Items (4)

Global planar dynamics with a star node and contracting nonlinearity ⋮ Limit Cycles for a Class of Zp-Equivariant Differential Systems ⋮ Revisiting limit cycles for 3-monomial differential equations ⋮ Limit cycles for 3-monomial differential equations

Cites Work

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• Limit cycles of polynomial systems with homogeneous non-linearities
• Metamorphoses of phase portraits of vector field in the case of symmetry of order 4
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• Limit Cycles for a Class of Abel Equations
• A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
• Bifurcation sequences at 1:4 resonance: an inventory
• Differential Equations Defined by the Sum of two Quasi-Homogeneous Vector Fields
• Phase Portraits of Planar Vector Fields: Computer Proofs

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