The S-dynamics in generalized covariant Hamiltonian system

Since the S-dynamics as a grand-new dynamics has been naturally discovered,  an attempt to deeply study the S-dynamics in the generalized covariant Hamiltonian system (GCHS) is made such as its properties and application for the quantum mechanics. We demonstrate a fact that the manifolds exist some properties such as wave-particle duality in quantum mechanics based on S-dynamics.