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Discrete point symmetries of ordinary differential equations. (English) Zbl 0923.34004
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.

MSC:
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
17B66Lie algebras of vector fields and related (super)algebras
34-04Machine computation, programs (ordinary differential equations)
68W30Symbolic computation and algebraic computation
20C40Computational methods (representations of groups)