Lie symmetries of the Lorenz model

Tanaji Sen, M. Tabor

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


We study the generalized symmetries of the Lorenz model to find the parameter values at which one or more time-dependent integrals of motion exist. In these cases the integrals are found trivially from the symmetries themselves. A complete study of the one completely algebraically integrable case shows: (a) the dynamics can be integrated exactly, by reducing it first to a lower-dimensional system; (b) the symmetry vector field is Hamiltonian. These facts hold for other dissipative, completely integrable dynamical systems as well. The analytic study of a natural two-form reveals that it is an entire function of time. The foliation of phase space induced by the two-form for the partially integrable cases has a simple description in terms of the coefficients occurring in the Laurent series expansions of the dependent variables.

Original languageEnglish (US)
Pages (from-to)313-339
Number of pages27
JournalPhysica D: Nonlinear Phenomena
Issue number3
StatePublished - Sep 1 1990
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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