The existence of Lie symmetries for first-order analytic discrete dynamical systems (Q1910041)

The synopsis translates some classical results into the terminology of Lie groups. It is mentioned in passing that the existence of a locally linearizing Lie transformation coincides with the existence of a solution of a nondegenerate Schrödinger functional equation. It is, however, not mentioned what neighbourhood of a singular point is transformed into the whole plane. It is also not mentioned that the corresponding solution of the Schrödinger equation is in general a transcendental function, much more complicated than any classical one. The absence of construction methods, deplored by the author, is therefore not astonishing.