Three-webs W(1, n, 1) and associated systems of ordinary differential equations

We consider a three-web on a smooth manifold formed by two n-parameter families of curves and a one-parameter family of hypersurfaces. For such webs, we define a family of adapted frames, find the systemof structure equations, and study the differential-geometric objects that arise in differential neighborhoods up to the third order. We prove that each system of ordinary differential equations (SODE) uniquely defines a three-web. This allows us to describe properties of a SODE in terms of the corresponding three-web. In particular, we characterize autonomous SODE.