Lorentzian anti-de Sitter plane
A.Z. Ali, Yu.L. Sachkov
TL;DR
This paper investigates the geometric control and optimality of trajectories on the two-dimensional Lorentzian anti-de Sitter plane, providing a detailed analysis of extremals, reachability, and Lorentzian distance.
Contribution
It introduces a comprehensive geometric control framework for the Lorentzian anti-de Sitter plane, including extremal trajectories and optimal synthesis construction.
Findings
Explicit extremal trajectories derived.
Reachable set characterized.
Lorentzian distance formula obtained.
Abstract
In this paper, we study a two-dimensional Lorentzian problem on the anti-de Sitter plane. Using methods of geometric control theory and differential geometry, it was possible to construct an orthonormal frame, calculate extremal trajectories, describe the reachable set, construct an optimal synthesis, and describe the Lorentzian distance.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra · Mathematics and Applications