Center conditions and integrable forms for the Poincaré problem

DOI10.1016/j.jmaa.2013.06.072zbMath1323.34043OpenAlexW2007016375MaRDI QIDQ2019072

G. R. Nicklason

Publication date: 27 March 2015

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.2013.06.072

zbMATH Keywords

integrable systemsAbel differential equationsymmetric centerscenter focus problem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (2)

Homogeneous-like generalized cubic systems ⋮ TWO GENERAL CENTRE PRODUCING SYSTEMS FOR THE POINCARÉ PROBLEM

Cites Work

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• Integrability of plane quadratic vector fields
• Integrable systems via polynomial inverse integrating factors
• The center problem for a linear center perturbed by homogeneous polynomials
• On the integrable rational Abel differential equations
• A general class of centers for the Poincaré problem
• Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
• Abel ODEs: Equivalence and integrable classes
• 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
• An Abel ordinary differential equation class generalizing known integrable classes
• A class of integrable polynomial vector fields

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