1210.3647 (Giampaolo Cicogna et al.)

A generalization of λ-symmetry reduction for systems of ODEs:
σ-symmetries    [PDF]

Giampaolo Cicogna, Giuseppe Gaeta, Sebastian Walcher

We consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the "invariants by differentiation" property, and can hence be used to reduce ODEs satisfying suitable invariance conditions in a fully algorithmic way, similarly to what happens for standard prolongations and symmetries.

View original: http://arxiv.org/abs/1210.3647