Melnikov Functions for a Class of Piecewise Hamiltonian Systems

Abstract

This paper is concerned with the number of limit cycles for a class of piecewise Hamiltonian systems with two zones separated by two semistraight lines. By constructing a Poincaré map, we obtain explicit expressions of the first, second and third order Melnikov functions. In addition, we apply their expressions to give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise polynomial Hamiltonian system.