Homoclinic points in symplectic and volume-preserving diffeomorphisms

Let M(n) be a compact n-dimensional manifold and omega be a symplectic or volume form on M(n). Let phi be a C-1 diffeomorphism on M(n) that preserves omega, and let p be a hyperbolic periodic point of phi. We show that generically p has a homoclinic point, and moreover, the homoclinic points of p is dense on both stable manifold and unstable manifold of p. Takens [11] obtained the same result for n = 2.