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Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8)
Yu. L. Sachkov, E. F. Sachkova Ailamazyan Program Systems Institute of RAS,
Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
Abstract:
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.
Received: 30.05.2019 Accepted: 01.10.2019
Citation:
Yu. L. Sachkov, E. F. Sachkova, “Symmetries and Parameterization of Abnormal Extremals in the Sub-Riemannian Problem with the Growth Vector (2, 3, 5, 8)”, Rus. J. Nonlin. Dyn., 15:4 (2019), 577–585
Linking options:
https://www.mathnet.ru/eng/nd685 https://www.mathnet.ru/eng/nd/v15/i4/p577
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Abstract page: | 167 | Full-text PDF : | 28 | References: | 15 |
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