Limit cycles bifurcated from piecewise Hamiltonian systems by Melnikov functions of any order.

This paper focuses on the research of the algorithm for higher order Melnikov functions for piecewise Hamiltonian systems under piecewise perturbations in any order ϵ. Then the formula is applied to the any order ϵ linear perturbations of a general center-center type piecewise linear system. The maximum number of zeros for any order Melnikov functions is 2 and it can be reached. It is worth mentioning that the algorithm can also be applied to smooth case. [ABSTRACT FROM AUTHOR]