Homoclinic orbits on compact hypersufaces in 293-1293-1293-1, of restricted contact type

Consider a smooth Hamiltonian system in ^2N , , the energy surface ={x/H(x)=H(0)} being compact, and 0 being a hyperbolic equilibrium. We assume, moreover, that {0} is of restricted contact type. These conditions are symplectically invariant. By a variational method, we prove the existence of an orbit homoclinic, i.e. non-constant and doubly asymptotic, to 0.