Title: Existence theorem for sub-Lorentzian problems

Authors: L.V.Lokutsievskiy, A.V.Podobryaev

Journal title: Journal of Dynamical and Control Systems

Year: 2024

Volume: 30

Pages: 10

Citation:

Lokutsievskiy, L.V., Podobryaev, A.V. Existence Theorem for Sub-Lorentzian Problems. J Dyn Control Syst 30, 10 (2024). https://doi.org/10.1007/s10883-024-09694-0

Abstract:

In this paper, we prove the existence theorem for longest paths in sub-Lorentzian problems, which generalizes the classical theorem for globally hyperbolic Lorentzian manifolds. We specifically address the case of invariant structures on homogeneous spaces, as the conditions for the existence theorem in this case can be significantly simplified. In particular, it turns out that longest paths exist for any left-invariant sub-Lorentzian structures on Carnot groups.