Properties of reachable sets in the sub-Lorentzian geometry
type: Item
instance of: scholarly article
title: Properties of reachable sets in the sub-Lorentzian geometry
zbMATH Open document ID: 1171.53023
author: Marek Grochowski
published in: Journal of Geometry and Physics
publication date: 2009-07-10T00:00:00Z
review text: This paper considers and obtains the classification of reachable sets from a given point in sub-Lorentzian geometry. For Lorentzian case and Sub-Lorentzian case, it gives some interesting results. This research is directly related to the study of sub-Riemannian geometry. In special case, one can construct the relationship between normal geodesics and singular geodesics with Hamiltonian geodesics.
reviewed by: Peibiao Zhao
Mathematics Subject Classification ID: 53C17
Mathematics Subject Classification ID: 53B20
zbMATH DE Number: 5577503
zbMATH Keywords: sub-Lorentzian manifolds
zbMATH Keywords: geodesics
zbMATH Keywords: reachable sets
zbMATH Keywords: geometric optimality
MaRDI profile type: Publication
full work available at URL: j.geomphys.2009.03.011
OpenAlex ID: W1967382362
Wikidata QID: Q125939486
cites work: The Large Scale Structure of Space-Time
cites work: Q4871706
cites work: Q3147594
cites work: Reachable sets for the Heisenberg sub-Lorentzian structure on \(\mathbb R^3\). An estimate for the distance function
cites work: Large deviations and the Malliavin calculus
cites work: Control theory from the geometric viewpoint.
cites work: Vector Fields on the n -Sphere
cites work: Q3312869
cites work: Q4335551
cites work: Functional analysis and time optimal control
cites work: Normal forms of germs of contact sub-Lorentzian structures on \(\mathbb R^3\). Differentiability of the sub-Lorentzian distance function
cites work: Q3531403
cites work: Shortest paths for sub-Riemannian metrics on rank-two distributions
cites work: Singular extremals on Lie groups
cites work: Genericity results for singular curves
cites work: Contrôlabilité des Systèmes non Linéaires
cites work: The Structure of Small-Time Reachable Sets in Low Dimensions
cites work: A Bang-Bang Theorem with Bounds on the Number of Switchings
DOI: 10.1016/J.GEOMPHYS.2009.03.011
description: scientific article; zbMATH DE number 5577503