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Zbl 0923.34004
Hydon, P.E.
Discrete point symmetries of ordinary differential equations. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 454, No.1975, 1961-1972 (1998). ISSN 1364-5021; ISSN 1471-2946/e

A constructive method is described which computes the discrete symmetries of an ordinary differential equation provided a Lie group of point symmetries is known. The method exploits the associated Lie algebra. First, the case of a one-dimensional Lie algebra is considered followed by the multidimensional case where extra properties are exploited. Various examples illustrate the method. The paper concludes with a proof that every ODE whose Lie group of point symmetries is isomorphic to the unimodular group has at least four inequivalent real discrete point symmetries.
[Karin Gatermann (Berlin)]

MSC 2000:: *34A25 Analytical theory of ODE
17B66 Lie algebras of vector fields and related algebras
34-04 Machine computation, programs (ordinary differential equations)
68W30 Symbolic computation and algebraic computation
20C40 Computational methods (representations of groups)

Keywords: differential equations; symmetry methods; constructive techniques; computer algebra; Lie groups

Cited in: Zbl 0969.34009

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