Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8)

The left-invariant sub-Riemannian problem with the growth vector (2, 3, 5, 8) is considered. A two-parameter group of infinitesimal symmetries consisting of rotations and dilations is described. The abnormal geodesic flow is factorized modulo the group of symmetries. A parameterization of the vertical part of abnormal geodesic flow is obtained.