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Dynamical systems embedded into Lie algebras

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2001-12
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American Institute of Physics
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Analytical and geometrical information on certain dynamical systems X is obtained under the assumption that X is embedded into a certain real Lie algebra.
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P. Olver, Applications of Lie Groups to Differential Equations (Springer, New York, 1986). G. Unal, Phys. Lett. A 260, 352 (1999); G. Jones, Nuovo Cimento Soc. Ital. Fis., B 112B, 1053 (1997); F. G. Gascon, Nuovo Cimento Soc. Ital. Fis., B 29, 73 (1980); M. Lutzky, J. Phys. A 12, 973 (1979). V. Arnold and A. Avez, Problemes Ergodiques de la Mecanique Classique (Gauthier-Villars, Paris, 1967); V. Arnold, Methodes Mathematiques de la Mecanique Classique (MIR, Moscow, 1976). Y. Choquet-Bruhat, C. DeWitt-Morette, and M. Dillard-Bleick, Analysis, Manifolds and Physics (North Holland, Amsterdam, 1978); B. Harrison and F. Estabrook, J. Math. Phys. 12, 653(1971). R. Abraham, Foundations of Mechanics (Benjamin, New York, 1967). T. Sen and M. Tabor, Physica D 44, 313 (1990); L. Dresner, J. Math. Phys. 12, 1339 (1971). N. Jacobson, Lie Algebras (Dover, New York, 1962); R. Gilmore, Lie Groups, Lie Algebras and Some of Their Applications(Wiley, New York, 1974). L. Eisenhart, Continuous Groups of Transformations (Princeton University Press, Princeton, NJ, 1933); S. Lie, Math. Ann. 25, 71 (1888); S. Lie and G. Scheffers, Vorlesungen uber differentialgleichungen mit bekanten infinitesimalen transformationen (Teubner, Leipzig, 1891). C. Sparrow, The Lorenz Equations: Bifurcation, Chaos and Strange Attractors (Springer, New York, 1982); E. Lorenz, Atmos. Sci. 20, 130 (1963); B. Hasard, J. Zhang, S. Hastings, and W. Troy, Appl. Math. Lett. 7, 79 (1994)
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