Lie symmetries of the Lorenz model

Tanaji Sen, Michael Tabor

Research output: Contribution to journalArticle

37 Citations (Scopus)

Abstract

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
Volume44
Issue number3
DOIs
StatePublished - Sep 1 1990
Externally publishedYes

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Hamiltonians
Lie Symmetry
Dynamical systems
Symmetry
symmetry
Laurent Expansion
entire functions
Laurent Series
dependent variables
Integrals of Motion
Foliation
Entire Function
series expansion
Series Expansion
dynamical systems
Phase Space
Vector Field
Dynamical system
Model
Dependent

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Lie symmetries of the Lorenz model. / Sen, Tanaji; Tabor, Michael.

In: Physica D: Nonlinear Phenomena, Vol. 44, No. 3, 01.09.1990, p. 313-339.

Research output: Contribution to journalArticle

Sen, Tanaji ; Tabor, Michael. / Lie symmetries of the Lorenz model. In: Physica D: Nonlinear Phenomena. 1990 ; Vol. 44, No. 3. pp. 313-339.
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