Computation of expansion coefficients of Melnikov functions near a nilpotent center

AbstractIn this paper, we consider the computation problem of expansion coefficients of Melnikov functions for near-Hamiltonian systems with a nilpotent center. We develop a general method for finding the computation formulas for the expansion coefficients. Based on the new method, an efficient algorithm is established to systematically compute the coefficients. Moreover, as an application we consider a kind of Liénard systems with a nilpotent center and study the number of limit cycles near the center