
Journal of Lie Theory 13 (2003), No. 1, 167188 Copyright Heldermann Verlag 2003 C ^{infinity}Symmetries and Reduction of Equations Without Lie Point Symmetries C. Muriel Dep. Matemáticas, Facultad de Ciencias, Universidad de Cádiz, 11510 Puerto Real, Cádiz, Spain J. L. Romero Dep. Matemáticas, Facultad de Ciencias, Universidad de Cádiz, 11510 Puerto Real, Cádiz, Spain It is proved that several usual methods of reduction for ordinary differential equations, that do not come from the Lie theory, are derived from the existence of C ^{infinity}  symmetries. This kind of symmetries is also applied to obtain two successive reductions of an equation that lacks Lie point symmetries but is a reduced equation of another one with a three dimensional Lie algebra of point symmetries. Some relations between C ^{infinity}  symmetries and potential symmetries are also studied. [ Fulltextpdf (237 KB)] for subscribers only. 