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

2019, Vol. 15, no. 4, pp.  577-585

Author(s): Sachkov Y. L., Sachkova E. F.

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.
Keywords: sub-Riemannian geometry, abnormal extremals, symmetries
Citation: Sachkov Y. L., Sachkova E. F., Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8), Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 4, pp.  577-585
DOI:10.20537/nd190417

## References

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