Critical Periods of Third-Order Planar Hamiltonian Systems

Periodic motion or oscillation is a common phenomenon which exists in almost all disciplines of physical and engineering systems. Limit cycle is one of the source generating periodic motion, and its study plays an important role in the research of nonlinear dynamical systems. A related wellknown problem to limit cycle is Hilbert’s 16th problem [Hilbert, 1902], which has attracted many mathematicians and scientists. Though the problem is far away from being completely solved, some progress has been recently achieved (e.g. see the review articles [Han, 2002; Li, 2003; Yu, 2006]). To be more specific, consider the following differential equations: { ẋ = Pn(x, y,α), ẏ = Qn(x, y,α), (1)