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Regular and Chaotic Dynamics, 2025, Volume 30, Issue 4, Pages 504–537
DOI: https://doi.org/10.1134/S1560354725040045 (Mi rcd1318) 		 
Special Issue: Celebrating the 75th Birthday of V.V. Kozlov (Issue Editors: Sergey Bolotin, Vladimir Dragović, and Dmitry Treschev)

The Lorentzian Anti-de Sitter Plane

Anton Z. Alia, Yuri L. Sachkovb

a Lomonosov Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia
b Ailamazyan Program Systems Institute RAS, RUDN University, 152020 Pereslavl-Zalessky, Russia
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DOI: https://doi.org/10.1134/S1560354725040045
Abstract: In this paper the two-dimensional Lorentzian problem on the anti-de Sitter plane is studied. Using methods of geometric control theory and differential geometry, we describe the reachable set, investigate the existence of Lorentzian length maximizers, compute extremal trajectories, construct an optimal synthesis, characterize Lorentzian distance and spheres, and describe the Lie algebra of Killing vector fields.
Keywords: Lorentzian geometry, geometric control theory, optimal control
Funding agency Grant number
Foundation for the Development of Theoretical Physics and Mathematics BASIS 23-7-1-16-1
The work is supported by the “Basis” Foundation, grant No. 23-7-1-16-1.
Received: 21.04.2025
Accepted: 15.07.2025
Document Type: Article
MSC: 53C50, 49K15
Language: English
Citation: Anton Z. Ali, Yuri L. Sachkov, “The Lorentzian Anti-de Sitter Plane”, Regul. Chaotic Dyn., 30:4 (2025), 504–537
Citation in format AMSBIB
\Bibitem{AliSac25}
\by Anton Z. Ali, Yuri L. Sachkov
\paper The Lorentzian Anti-de Sitter Plane
\jour Regul. Chaotic Dyn.
\yr 2025
\vol 30
\issue 4
\pages 504--537
\mathnet{http://mi.mathnet.ru/rcd1318}
\crossref{https://doi.org/10.1134/S1560354725040045}
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