References
A. M. Vershik and V. Ya. Gershkovich, in Dynamical Systems. VII, Encycl. Math. Sci. (Springer- Verlag, Berlin, 1994), Vol. 16, pp. 1–81.
V. Jurdjevic, Geometric Control Theory (Cambridge Univ. Press, Cambridge, 1997).
R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications (Amer. Math. Soc., Providence, RI, 2002).
A. A. Agrachev and Yu. L. Sachkov, Control Theory from the Geometric Viewpoint (Springer- Verlag, Berlin, 2004).
A. Agrachev, D. Barilari and U. Boscain, A Comprehensive Introduction to Sub-Riemannian Geometry (Cambridge Univ. Press, Cambridge, 2019).
Yu. L. Sachkov, Introduction to Geometric Control (Springer, Cham, 2022).
M. Grochowski, in Geometric Singularity Theory, Banach Center Publ. (Polish Acad. Sci. Inst. Math., 2004), Vol. 65, pp. 57–65.
M. Grochowski, J. Dyn. Control Syst. 12 (2), 145 (2006).
Acknowledgments
The authors are grateful to A. A. Agrachev and L. V. Lokutsievskii for useful discussions of the problem under consideration. The authors also thank the referee for useful comments concerning the presentation in the paper.
Funding
This research was supported by the Russian Science Foundation under grant 22-11-00140, https://rscf.ru/project/22-11-00140/.
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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 154–157 https://doi.org/10.4213/mzm13859.
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Sachkov, Y.L., Sachkova, E.F. Sub-Lorentzian Problem on the Heisenberg Group. Math Notes 113, 159–162 (2023). https://doi.org/10.1134/S0001434623010182
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DOI: https://doi.org/10.1134/S0001434623010182