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


AUTHORS:
Inmaculada Baldoma

Dept. d'Enginyeria Informatica i Matematiques.
Campus Sescelades Avinguda dels Paisos Catalans, 26 43007 Tarragona, SPAIN

E-mails: immaculada.baldoma@upc.edu

ABSTRACT:

We consider families of one and a half degrees of freedom rapidly forced
Hamiltonian system which are perturbations of one degree of freedom
Hamiltonians having a homoclinic connection. We derive the inner equation for
this class of Hamiltonian system which is expressed as the Hamiltonian-Jacobi
equation of one a half degrees of freedom Hamiltonian. The inner equation
depends on a parameter not necessarily small.  We prove the existence of
special solutions of the inner equation with a given behavior at infinity. We
also compute the asymptotic expression for the difference between these
solutions. In some perturbative cases, this asymptotic expression is strongly
related with the Melnikov function associated to our initial Hamiltonian.