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Critical periods of a periodic annulus linking to equilibria at infinity in a cubic system. (English) Zbl 1180.34034

The authors investigate critical periods for a planar cubic differential system with a periodic annulus linking to equilibria at infinity. They derive a Picard-Fuchs equation from a system of abelian integrals and a Riccati equation for a ratio of derivatives of abelian integrals.

MSC:

34C08 Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.)
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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