## Abstract

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 general Ngroup, G_{N}, and prove that it has certain similar properties. A particular property of G_{N} is that as a Lie group dim (G_{N})≥1. Certain properties of its Lie-algebra gjv 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.

Original language | English |
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Pages (from-to) | 475-483 |

Number of pages | 9 |

Journal | Acta Mathematicae Applicatae Sinica |

Volume | 17 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2001 |

## Scopus Subject Areas

- Applied Mathematics

## User-Defined Keywords

- Hamiltonian control systems
- Hamiltonian systems
- Symplectic algebra
- Symplectic algorithm
- Symplectic group