LIMIT CYCLES FROM A CUBIC REVERSIBLE SYSTEM VIA THE THIRD-ORDER AVERAGING METHOD

This article concerns the bifurcation of limit cycles from a cubic integrable and non-Hamiltonian system. By using the averaging theory of the first and second orders, we show that under any small cubic homogeneous perturbation, at most two limit cycles bifurcate from the period annulus of the unperturbed system, and this upper bound is sharp. By using the averaging theory of the third order, we show that two is also the maximal number of limit cycles emerging from the period annulus of the unperturbed system.