On generalized hamiltonian systems

The purpose of this paper is to explore an extension of some fundamental properties of the Hamiltonian systems to a more general case. We first extend symplectic group to a generalN-group,GN, and prove that it has certain similar properties. A particular property ofGN is that as a Lie group dim (GN)≥1. Certain properties of its Lie-algebragN are investigated. The results obtained are used to investigate the structure-preserving systems, which generalize the property of symplectic form preserving of Hamiltonian system to a covariant tensor field preserving of certain dynamic systems. The results provide a theoretical benchmark of applying symplectic algorithm to a considerably larger class of structure-preserving systems.