Twisted prolongations and the NC-variations

Abstract

In the year 2001, Spanish mathematicians C.Murial and J.Romero, introduced the new procedure of prolongations of vector fields from the space Y, of a configuration bundle π : Y → R to the jet spaces J ^k(π) (λ-prolongations), new class of “symmetries” (λ-symmetries) for the ordinary differential equations and the new method of the symmetry reduction of the ordinary differential equations ([102]) with the λ-symmetries corresponding to the λ-prolongations.