A reduction method of ODEs not possessing Lie point symmetries makes use of the so called $\lambda$-symmetries. These symmetries are not standard symmetries, nevertheless for any given $\lambda$-symmetry of an ODE $% \mathcal{Y}$ one can always reconstruct nonlocal symmetries of $\mathcal{Y}$% . As a consequence, using these nonlocal symmetries, the $\lambda$-symmetry reduction method follows from the standard method of symmetry reduction by differential invariants.
Nonlocal interpretation of [lambda]-symmetries / D. Catalano Ferraioli - In: Symmetry and Perturbation Theory / [a cura di] Giuseppe Gaeta, Sebastian Walcher, Raffaele Vitolo. - Singapore : World Scientific, 2008 Feb. - ISBN 978-981-277-616-7. - pp. 241-242 (( Intervento presentato al 6. convegno SYMMETRY AND PERTURBATION THEORY tenutosi a Otranto nel 2007.
Nonlocal interpretation of [lambda]-symmetries
D. Catalano FerraioliPrimo
2008
Abstract
A reduction method of ODEs not possessing Lie point symmetries makes use of the so called $\lambda$-symmetries. These symmetries are not standard symmetries, nevertheless for any given $\lambda$-symmetry of an ODE $% \mathcal{Y}$ one can always reconstruct nonlocal symmetries of $\mathcal{Y}$% . As a consequence, using these nonlocal symmetries, the $\lambda$-symmetry reduction method follows from the standard method of symmetry reduction by differential invariants.
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