Equivalence of scalar ODEs under contact, point and fiber-preserving transformations

It is known that the equivalence problem for scalar ODEs of order 3 and higher can be solved via the construction of a canonical Cartan connection. The invariants then appear as part of the curvature of this connection. This allows to describe explicitly all scalar ODEs of order 3 and higher that can be brought to the trivial equation by contact transformations. The goal of this talk is to show how most of this story can be extended to the equivalence of scalar ODEs under point and fiber-preserving transformations.