Bounding the number of limit cycles for perturbed piecewise linear Hamiltonian system (Q6635228)

The authors investigate the number of limit cycles for piecewise linear Hamiltonian system with a homoclinic loop under perturbations of piecewise smooth polynomials. This is closely related to the Hillbert's 16th problem. The method of this paper is a kind of generalization of Melnikov method from smooth systems to nonsmooth ones. After getting the number of zeros of the first order Melnikov function, the authors obtain the exact number of limit cycles bifurcating from a periodic annulus.