Homoclinic orbits of a Hamiltonian system

Abstract.

We establish existence results of homoclinic orbits of the first order time-dependent Hamiltonian system $\dot z = {\Cal J} H_z (t, z),$ where H(t, z) depends periodically on $t, H(t, z) = \frac{1}{2} z{\Cal L} (t) z + W (t, z), L(t)$ is a symmetric matrix valued function and W(t, z) satisfies certain global superquadratic condition. We relax partly the assumption often used before: L is independent of t and $sp({\Cal J} L)\cap i\Bbb{R} = \phi.$