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Symmetry group classification of ordinary differential equations: Survey of some results. (English) Zbl 1135.34029
After the famous results of Sophus Lie on symmetry analysis of ordinary differential equations several results on point symmetry group analysis have been obtained, particularly by P. Leach. This article presents a review on the point symmetry group properties of linear nth order (n1) differential equations as well as the point symmetry group classification of scalar second order ODEs both in the real and complex domains. Many references are given to the papers of P. Leach on well-researched equations and related results on classification and integrability together with some open problem in this domain.
MSC:
34C14Symmetries, invariants (ODE)
34C20Transformation and reduction of ODE and systems, normal forms
34A30Linear ODE and systems, general
70H33Symmetries and conservation laws, reverse symmetries, invariant manifolds, etc.