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Russian Journal of Nonlinear Dynamics, 2024, Volume 20, Number 4, Pages 619–633
DOI: https://doi.org/10.20537/nd241103 (Mi nd914) 		 
The Lorentzian Problem on 2-Dimensional de Sitter Space

V. S. Petukhov, Yu. L. Sachkov

Ailamazyan Program Systems Institute, Russian Academy of Sciences, Pereslavl-Zalessky, Yaroslavl Region, 152020 Russia
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DOI: https://doi.org/10.20537/nd241103
Abstract: This paper considers the Lorentzian optimal control problem on two-dimensional de Sitter space. Normal and abnormal optimal trajectories are studied using the Pontryagin maximum principle. Attainable sets, spheres and distance in the Lorentzian metric are computed. Killing vector fields and isometries are described.
Keywords: Lorentzian geometry, de Sitter space, optimal control
Funding agency Grant number
Russian Science Foundation 22-11-00140
This work was supported by the Russian Science Foundation under grant 22-11-00140 (https://rscf.ru/project/22-11-00140/), and performed at the Ailamazyan Program Systems Institute of the Russian Academy of Sciences.
Received: 25.12.2023
Accepted: 30.07.2024
Document Type: Article
MSC: 53C50, 49K15
Language: English
Citation: V. S. Petukhov, Yu. L. Sachkov, “The Lorentzian Problem on 2-Dimensional de Sitter Space”, Rus. J. Nonlin. Dyn., 20:4 (2024), 619–633
Citation in format AMSBIB
\Bibitem{PetSac24}
\by V. S. Petukhov, Yu. L. Sachkov
\paper The Lorentzian Problem on 2-Dimensional de Sitter Space
\jour Rus. J. Nonlin. Dyn.
\yr 2024
\vol 20
\issue 4
\pages 619--633
\mathnet{http://mi.mathnet.ru/nd914}
\crossref{https://doi.org/10.20537/nd241103}
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