A generalization of \lambda-symmetry reduction for systems of ODEs:   \sigma-symmetries
  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. 
Giampaolo Cicogna, Giuseppe Gaeta, Sebastian Walcher
math-ph math.MP