λ−Symmetries and linearization of ordinary differential equations through nonlocal transformations ?

A recent study (Muriel and Romero (2010a)) on the linearization of ordinary differential equations through generalized Sundman transformations suggests considering the problem of linearization through nonlocal transformations from the point of view of the λ−symmetries admitted by the equation and their associated first integrals. The systematic methods to calculate λ−symmetries and associated first integrals of the ordinary differential equations provide well-defined algorithms to calculate the linearizing nonlocal transformations. Several examples, including differential equations with trivial algebra of Lie point symmetries, illustrate the presented methods.