Front Asymptotics of a Flat Sub-Riemannian Structure on the Engel Distribution

We approximate the front of a flat sub-Riemannian structure on the Engel distribution in a neighborhood of a non-subanalytic singularity by the front of a control system integrable in elementary functions. As a corollary, we find the asymptotics of the exponential map of a flat sub-Riemannian structure on the Engel distribution.