Melnikov Functions for a Class of Piecewise Hamiltonian Systems (Journal of Nonlinear Modeling and Analysis, 2024)
This paper is concerned with the number of limit cycles for aclass of piecewise Hamiltonian systems with two zones separated by two semistraight lines. By constructing a Poincaré map, we obtain explicit expressionsof the first, second and third order Melnikov functions. In addition, we applytheir expressions to give upper bounds of the number of limit cycles bifurcatedfrom a period annulus of a piecewise polynomial Hamiltonian system.