Fundamental invariants of systems of ODEs of higher order

We find the complete set of fundamental invariants for systems of ordinary differential equations of order >= 4 under the group of point transformations generalizing similar results for contact invariants of a single ODE and point invariants of systems of the second and the third order. It turns out that starting from systems of order (k + 1) >= 4, the complete set of fundamental invariants is formed by k generalized Wilczynski invariants coming from the linearized system and an additional invariant of degree 2.