Sub-Lorentzian geometry on the Martinet distribution

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

Two problems of sub-Lorentzian geometry on the Martinet distribution are studied. For the first, the reachability set has a nontrivial intersection with the Martinet plane, but for the second it does not. Reachable sets, optimal trajectories, sub-Lorentzian distances and spheres are described.

作者简介

Yu. Sachkov

A.K. Ailamazyan Program Systems Institute of the Russian Academy of Sciences

编辑信件的主要联系方式.
Email: yusachkov@gmail.com
俄罗斯联邦

参考

  1. Montgomery R. A tour of subriemannnian geometries, their geodesics and applications // Amer. Math. Soc. 2002.
  2. Agrachev A., Barilari D., Boscain U. A Comprehensive Introduction to sub-Riemannian Geometry from Hamiltonian viewpoint // Cambridge Studies in Advanced Mathematics. Cambridge: Cambridge Univ. Press, 2019.
  3. Grochowski M. Geodesics in the sub-Lorentzian geometry // Bull. Polish. Acad. Sci. Math. 2002. V. 50.
  4. Grochowski M. Normal forms of germs of contact sub-Lorentzian structures on . Differentiability of the sub-Lorentzian distance // J. Dynam. Control Systems. 2003. V. 9. № 4.
  5. Grochowski M. Properties of reachable sets in the sub-Lorentzian geometry // J. Geom. Phys. 2009. V. 57. № 9. P. 885–900.
  6. Grochowski M. Reachable sets for contact sub-Lorentzian metrics on . Application to control affine systems with the scalar input // J. Math. Sci. (N.Y.) 2011. V. 177. № 3. P. 383–394.
  7. Grochowski M. On the Heisenberg sub-Lorentzian metric on // Geometric Singularity Theory. Banach Center Publications, Institute of Mathematics. Warsawa: Polish Academy of Sciences, 2004. V. 65.
  8. Grochowski M. Reachable sets for the Heisenberg sub-Lorentzian structure on . An estimate for the distance function // Journal of Dynamical and Control Systems. 2006. V. 12. № 2. P. 145–160.
  9. Chang D.-C., Markina I. and Vasil'ev A. Sub-Lorentzian geometry on anti-de Sitter space // J. Math. Pures Appl. 2008. V. 90. P. 82–110.
  10. Korolko A. and Markina I. Nonholonomic Lorentzian geometry on some H-type groups // J. Geom. Anal. 2009. V. 19. P. 864–889.
  11. Grong E., Vasil’ev A. Sub-Riemannian and sub-Lorentzian geometry on SU(1, 1) and on its universal cover // J. Geom. Mech. 2011. V. 3. № 2. P. 225–260.
  12. Grochowski M., Medvedev A., Warhurst B. 3-dimensional left-invariant sub-Lorentzian contact structures // Differential Geometry and its Applications. 2016. V. 49. P. 142–166.
  13. Sachkov Yu. L., Sachkova E.F. Sub-Lorentzian distance and spheres on the Heisenberg group // Journal of Dynamical and Control Systems. 2023. V. 29. P. 1129–1159.
  14. Аграчев А.А., Сачков Ю.Л. Геометрическая теория управления. Физматлит, 2005. Перевод: Agrachev A.A., Sachkov Yu.L. Control Theory from the Geometric Viewpoint. Springer, 2004.
  15. Сачков Ю.Л. Введение в геометрическую теорию управления. М.: URSS, 2021. Расширенный перевод: Sachkov Yu. Introduction to geometric control. Springer, 2022.
  16. Agrachev A., Bonnard B., Chyba M., Kupka I. Sub-Riemannian sphere in Martinet flat case // J. ESAIM: Control, Optimisation and Calculus of Variations. 1997. V. 2. P. 377–448.
  17. Сачков Ю.Л. Левоинвариантные задачи оптимального управления на группах Ли, интегрируемые в эллиптических функциях // УМН. 2023. Т. 78. № 1 (469). С. 67–166.

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2024