TY - JOUR

T1 - Lie symmetries of the Lorenz model

AU - Sen, Tanaji

AU - Tabor, M.

N1 - Funding Information:
This work was supported by the US Department of Energy Grant No. DE-FG02-84ER13190. TS would like to thank Amitava Bhattacharjee for some valuable conversations and comments on the manuscript and Jos6 Milovich for useful discussions and help with some computer algebra. MT is an Alfred P. Sloan Research Fellow.

PY - 1990/9/1

Y1 - 1990/9/1

N2 - 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.

AB - 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.

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U2 - 10.1016/0167-2789(90)90152-F

DO - 10.1016/0167-2789(90)90152-F

M3 - Article

AN - SCOPUS:0000587469

VL - 44

SP - 313

EP - 339

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3

ER -