Infinitely Many Large Amplitude Homoclinic Orbits for a Class of Autonomous Hamiltonian Systems

For a class of fourth order autonomous Hamiltonian systems, we give geometrical conditions that imply the existence of infinitely many homoclinic orbits to a saddle-focus equilibrium. Our results are global in the sense that they do not rely on any transversality assumption. They are applied to two example systems; one arises in elasticity and in water-wave theory, the other describes the motion of a particle in a certain rotating potential.