Algebraic integrability and generalized symmetries of dynamical systems

Unal G.

PHYSICS LETTERS A, vol.260, no.5, pp.352-359, 1999 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 260 Issue: 5
  • Publication Date: 1999
  • Doi Number: 10.1016/s0375-9601(99)00531-9
  • Journal Name: PHYSICS LETTERS A
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.352-359
  • Istanbul Technical University Affiliated: No


It has been shown that when an n-dimensional dynamical system admits a generalized symmetry vector field which involves a divergence-free Liouville vector field, then it possesses n - 1 independent first integrals (i.e., it is algebraically integrable). Furthermore, the Liouville vector field can be employed for the classification of algebraically integrable dynamical systems. The results have been discussed on examples which arise in physics. (C) 1999 Elsevier Science B.V. All rights reserved.