On generalized hamiltonian systems

Daizhan Cheng*, Weimin Xue, Lizhi LIAO, Dayong Cai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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, GN, and prove that it has certain similar properties. A particular property of GN is that as a Lie group dim (GN)≥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 languageEnglish
Pages (from-to)475-483
Number of pages9
JournalActa Mathematicae Applicatae Sinica
Volume17
Issue number4
DOIs
Publication statusPublished - 2001

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Hamiltonian control systems
  • Hamiltonian systems
  • Symplectic algebra
  • Symplectic algorithm
  • Symplectic group

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