Degenerate abnormal trajectories in a sub-Riemannian problem with growth vector (2, 3, 5, 8)

We consider the nilpotent sub-Riemannian problem with growth vector (2, 3, 5, 8). We describe and study abnormal extremals orthogonal to the cube of the distribution. We analyze the geometric properties of a two-dimensional surface in the state space on which the corresponding abnormal trajectories define optimal synthesis. © 2017, Pleiades Publishing, Ltd.