Horseshoes for autonomous Hamiltonian systems using the Melnikov integral

Abstract

This paper applies the Melnikov method to autonomous perturbations of completely integrable Hamiltonian systems. The forcing of the perturbed system is caused by internal oscillations which are not necessarily decoupled. A unified treatment is presented which relates some results of Holmes and Marsden with a result of Lerman and Umanskii. It is also shown that two forms of the Melnikov function by integrals are in fact equal.