Geodesic
C infinity-Symmetries and Reduction of Equations Without Lie Point Symmetries
Journal of Lie theory, Tome 13 (2003) no. 1, pp. 167-188 Cet article a éte moissonné depuis la source Heldermann Verlag

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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. 
@article{JLT_2003_13_1_JLT_2003_13_1_a9,
     author = {C. Muriel and J. L. Romero },
     title = {C {\protect\textsuperscript{infinity}-Symmetries} and {Reduction} of {Equations} {Without} {Lie} {Point} {Symmetries}},
     journal = {Journal of Lie theory},
     pages = {167--188},
     year = {2003},
     volume = {13},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2003_13_1_JLT_2003_13_1_a9/}
}
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C. Muriel; J. L. Romero . C infinity-Symmetries and Reduction of Equations Without Lie Point Symmetries. Journal of Lie theory, Tome 13 (2003) no. 1, pp. 167-188. http://geodesic.mathdoc.fr/item/JLT_2003_13_1_JLT_2003_13_1_a9/