Center conditions for a lopsided quartic polynomial vector field

DOI10.1016/S0007-4497(02)01114-4zbMath1015.34016OpenAlexW2045172628MaRDI QIDQ1612747

Roland Pons, Nazim Salih

Publication date: 13 July 2003

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0007-4497(02)01114-4

zbMATH Keywords

centerreturn mapquartic polynomial vector field

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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 (9)

Center, limit cycles and isochronous center of a \(Z_{4}\)-equivariant quintic system ⋮ A new method to determine isochronous center conditions for polynomial differential systems. ⋮ The isochronous center for Kukles homogeneous systems of degree eight ⋮ CENTERS FOR THE KUKLES HOMOGENEOUS SYSTEMS WITH EVEN DEGREE ⋮ Center and isochronous center at infinity for differential systems. ⋮ Center conditions for a lopsided quintic polynomial vector field ⋮ The isochronous centers for Kukles homogeneous system of degree nine ⋮ Center conditions and bifurcation of limit cycles for a class of fifth degree systems ⋮ Analytic Integrability of Two Lopsided Systems

Cites Work

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• The number of limit cycles of certain polynomial differential equations
• Degenerate Hopf Bifurcation Formulas and Hilbert’s 16th Problem
• On a certain generalization of Bautin's theorem
• Successive derivatives of a first return map, application to the study of quadratic vector fields

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