Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle

الملخص EN

We study the expansions of the first order Melnikov functions for general near-Hamiltonian systems near a compound loop with a cusp and a nilpotent saddle.

We also obtain formulas for the first coefficients appearing in the expansions and then establish a bifurcation theorem on the number of limit cycles.

As an application example, we give a lower bound of the maximal number of limit cycles for a polynomial system of Liénard type.