2N dimensional Canonical Systems

Some important properties of solutions of any periodic and non periodic 2N dimensional canonical system are established. Also, the eigenvalue problem associated to the systems is considered. To this end, we prove the existence of solution, show that the fundamental matrix is symplectic. We obtain a solution that decay at infinity or psudo-periodic to a periodic canonical system. We relate the systems to a self-adjoint operator on a Hilbert space and show that the eigenfunctions form an orthonormal basis