Differential Invariants of Second Order ODEs, I

This paper is devoted to differential invariants of equations w.r.t. point transformations. The natural bundle of these equations and its bundles of k -jets of sections, k =0,1,2,…, are considered. The action of the pseudogroup of all point transformations on these bundles is investigated. Tensor differential invariants distinguishing orbits of this action on jet bundles of second and third orders are constructed. A complete collection of generators and their differential syzygies is obtained for the algebra of all scalar differential invariants of a wide class of considered equations containing generic equations.