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Program Systems: Theory and Applications, 2016, Volume 7, Issue 4, Pages 161–176 (Mi ps237)  

Optimization Methods and Control Theory

Asymptotics of a section by a plane of the sub-Riemannian sphere on the Engel group near abnormal trajectory

A. Yu. Popov

Ailamazyan Program Systems Institute of RAS

Abstract: In this paper we compute an asymptotics of the curve that is the intersection of the unit sub-Riemannian sphere on the Engel group with the subspace $\{x=z=0\}$ near the abnormal trajectory. It follows from the asymptotics that this curve is not analytic at the point $(1, 0, 0, 0)$. (In Russian).

Key words and phrases: sub-Riemannian structure, elliptic integrals, asymptotics.

Full text: PDF file (747 kB)
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UDC: 517.977
Received: 17.10.2016
Accepted: 16.12.2016

Citation: A. Yu. Popov, “Asymptotics of a section by a plane of the sub-Riemannian sphere on the Engel group near abnormal trajectory”, Program Systems: Theory and Applications, 7:4 (2016), 161–176

Citation in format AMSBIB
\Bibitem{Pop16}
\by A.~Yu.~Popov
\paper Asymptotics of a section by a plane of the sub-Riemannian sphere on the Engel group near abnormal trajectory
\jour Program Systems: Theory and Applications
\yr 2016
\vol 7
\issue 4
\pages 161--176
\mathnet{http://mi.mathnet.ru/ps237}


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