The inner equation for one and a half degrees of freedom rapidly forced Hamiltonian systems

We consider families of one and a half degrees of freedom rapidly forced Hamiltonian systems which are perturbations of one degree of freedom Hamiltonians with a homoclinic connection. We derive the inner equation for this class of Hamiltonian system which is expressed as the Hamiltonian–Jacobi equation of a one a half degrees of freedom Hamiltonian. The inner equation depends on a parameter not necessarily small.