Critical periods of a periodic annulus linking to equilibria at infinity in a cubic system
Zhirong He Weinian Zhang
Discrete & Continuous Dynamical Systems - A 2009, 24(3): 841-854 doi: 10.3934/dcds.2009.24.841
In this paper we investigate critical periods for a planar cubic differential system with a periodic annulus linking to equilibria at infinity. The monotonicity of the period function is decided by the sign of the second order derivative of a Abelian integral. We derive a Picard-Fuchs equation from a system of Abelian integrals and further give an induced Riccati equation for a ratio of derivatives of Abelian integrals. The number of critical points of the period function for periodic annulus is determined by discussing an planar autonomous system, the orbits of which describe solutions of the Riccati equation.
keywords: critical period Riccati equation. Abelian integral cubic system Hamiltonian system Picard-Fuchs equation

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