He, Zhirong; Zhang, Weinian Critical periods of a periodic annulus linking to equilibria at infinity in a cubic system. (English) Zbl 1180.34034 Discrete Contin. Dyn. Syst. 24, No. 3, 841-854 (2009). 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. Reviewer: Valery A. Gaiko (Minsk) Cited in 1 Document 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 Keywords:planar cubic differential system; critical period; abelian integral; Picard-Fuchs equation; Riccati equation PDFBibTeX XMLCite \textit{Z. He} and \textit{W. Zhang}, Discrete Contin. Dyn. Syst. 24, No. 3, 841--854 (2009; Zbl 1180.34034) Full Text: DOI