A general class of centers for the Poincaré problem

DOI10.1016/j.jmaa.2009.04.047zbMath1190.34034OpenAlexW2051825792MaRDI QIDQ1029130

G. R. Nicklason

Publication date: 9 July 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.04.047

zbMATH Keywords

Abel differential equationcenter-focus problemsymmetric centers

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14)

Related Items

Homogeneous-like generalized cubic systems ⋮ Sufficient and necessary center conditions for the Poincaré systems \(P(2, 2n) (n \leq 5)\) ⋮ Center conditions and integrable forms for the Poincaré problem

Cites Work

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• Integrability of plane quadratic vector fields
• The center problem for a linear center perturbed by homogeneous polynomials
• Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
• Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
• Polynomial first integrals via the Poincaré series
• Integrable systems in the plane with center type linear part
• Polynomial first integrals of systems in the plane with center type linear part

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