电邮这篇文章 Explicit formulae for extremals in sub-Lorentzian and Finsler problems on 2D and 3D Lie groups
- 作者: Ladeishchikov E.A.1, Lokutsievskiy L.V.2, Prilepin N.V.1
-
隶属关系:
- Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
- Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
- 期: 卷 216, 编号 12 (2025)
- 页面: 79-124
- 栏目: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/358685
- DOI: https://doi.org/10.4213/sm10355
- ID: 358685
如何引用文章
开放存取
##reader.subscriptionAccessGranted##
订阅存取
详细
Questions relating to the search of geodesics in a series of left-invariant problems with sub-Lorentzian and Finsler structure are under consideration. Explicit formulae for extremals are found in terms of trigonometric functions of convex trigonometry. In sub-Lorentzian problems the machinery of the new trigonometric functions $\sinh_\Omega$ and $\cosh_\Omega$ , generalizing $\sinh$ and $\cosh$ to the case of an unbounded convex set $\Omega\subset\mathbb R^2$ , is particularly useful.
作者简介
Evgeny Ladeishchikov
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Email: evgen310864@gmail.com
without scientific degree, no status
Lev Lokutsievskiy
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Email: lion.lokut@gmail.com
ORCID iD: 0000-0002-8083-4296
Scopus 作者 ID: 35148203500
Researcher ID: ABE-7153-2021
Doctor of physico-mathematical sciences, no status
Nikita Prilepin
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
Email: nickprilepin@yandex.ru
参考
- M. Grochowski, “Geodesics in the sub-Lorentzian geometry”, Bull. Polish Acad. Sci. Math., 50:2 (2002), 161–178
- M. Grochowski, “Properties of reachable sets in the sub-Lorentzian geometry”, J. Geom. Phys., 59:7 (2009), 885–900
- Der-Chen Chang, I. Markina, A. Vasil'ev, “Sub-Lorentzian geometry on anti-de Sitter space”, J. Math. Pures Appl. (9), 90:1 (2008), 82–110
- E. Grong, A. Vasil'ev, “Sub-Riemannian and sub-Lorentzian geometry on $operatorname{SU}(1,1)$ and on its universal cover”, J. Geom. Mech., 3:2 (2011), 225–260
- A. Korolko, I. Markina, “Nonholonomic Lorentzian geometry on some $mathbb H$-type groups”, J. Geom. Anal., 19:4 (2009), 864–889
- V. Yu. Protasov, “Antinorms on cones: duality and applications”, Linear Multilinear Algebra, 70:22 (2022), 7387–7413
- A. A. Ardentov, L. V. Lokutsievskiy, Yu. L. Sachkov, “Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry”, ESAIM Control Optim. Calc. Var., 27 (2021), 32, 52 pp.
- Yu. L. Sachkov, “Lorentzian distance on the Lobachevsky plane”, Nonlinearity, 37:9 (2024), 095027, 35 pp.
- A. Agrachev, D. Barilari, “Sub-Riemannian structures on 3D Lie groups”, J. Dyn. Control Syst., 18:1 (2012), 21–44
- L. V. Lokutsievskiy, “Explicit formulae for geodesics in left-invariant sub-Finsler problems on Heisenberg groups via convex trigonometry”, J. Dyn. Control Syst., 27:4 (2021), 661–681
补充文件
