Symmetries, integrating factors and Nambu mechanics

Unal G.

PHYSICS LETTERS A, vol.223, no.5, pp.355-358, 1996 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 223 Issue: 5
  • Publication Date: 1996
  • Doi Number: 10.1016/s0375-9601(96)00771-2
  • Journal Name: PHYSICS LETTERS A
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.355-358
  • Istanbul Technical University Affiliated: No

Abstract

We show that if an n-dimensional autonomous dynamical system (DS) with a vector field (VF) which has constant divergence possesses n - 1 independent first integrals, then it admits a symmetry VF which involves Nambu mechanics (NM). If the DS is conservative, then the Nambu VF happens to be a symmetry VF of the DS. We also show that the integrating factors can be constructed via NM. We illustrate our results on the Lotka-Volterra DS.