The Number of Limit Cycles Bifurcating from a Piecewise-Linear Hamiltonian System with a Saddle

In this paper, we investigate limit cycle bifurcations from certain piecewise-linear Hamiltonian systems with at least one saddle under perturbations of piecewise polynomials. Using the Melnikov function method for piecewise smooth systems, we obtain upper and lower bounds of the maximum number of limit cycles that bifurcate from periodic annuli.