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,G _N , and prove that it has certain similar properties. A particular property ofG _N is that as a Lie group dim (G _N )≥1. Certain properties of its Lie-algebrag _N 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. This research is partly supported by National Natural Science Foundation of China (No. G59837270, G1998020308) and the National Key Project of China.