Integrable systems via polynomial inverse integrating factors

DOI10.1016/S0007-4497(02)01111-9zbMath1016.34026MaRDI QIDQ698171

Jaume Giné, Maite Grau, Javier Chavarriga

Publication date: 18 September 2002

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

zbMATH Keywords

planar polynomial vector fieldperiodic orbitintegrating factorcenter-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) Dynamics induced by flows and semiflows (37C10)

Related Items (6)

An Improvement on the Number of Limit Cycles Bifurcating from a Nondegenerate Center of Homogeneous Polynomial Systems ⋮ A survey on the inverse integrating factor ⋮ Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers ⋮ Limit cycle bifurcations from a non-degenerate center ⋮ Higher order limit cycle bifurcations from non-degenerate centers ⋮ Center conditions and integrable forms for the Poincaré problem

Cites Work

• A method of constructing cycles without contact around a weak focus
• Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
• Integrability of a linear center perturbed by a fourth degree homogeneous polynomial
• Integrable systems in the plane with center type linear part
• On the nonexistence, existence and uniqueness of limit cycles
• On a certain generalization of Bautin's theorem
• A class of integrable polynomial vector fields
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