Sub-Lorentzian structures in \(\mathbb {R}^4\): left-invariance and conformal normal forms

DOI10.1007/s10883-018-9396-9zbMath1492.53044OpenAlexW2791134265MaRDI QIDQ721991

I. A. Bogaevskii

Publication date: 20 July 2018

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10883-018-9396-9

zbMATH Keywords

normal formsattainable setsconformal equivalencecontrol-affine systemsgeometrically optimal trajectoriesleft-invariancesub-Lorentzian and sub-Riemannian structures

Mathematics Subject Classification ID

Attainable sets, reachability (93B03) Sub-Riemannian geometry (53C17)

Related Items (3)

Fronts of control-affine systems in R^3 ⋮ Causality and topology in sub-Lorentzian geometry ⋮ On the effect of intersection of characteristics in a two-dimensional massless Dirac equation with linear potential and localized initial condition

Cites Work

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• Properties of reachable sets in the sub-Lorentzian geometry
• Nonholonomic Lorentzian geometry on some \(\mathbb H\)-type groups
• Normal forms of germs of contact sub-Lorentzian structures on \(\mathbb R^3\). Differentiability of the sub-Lorentzian distance function
• Control theory from the geometric viewpoint.
• Exponential mappings for contact sub-Riemannian structures
• Reachable sets for contact sub-Lorentzian structures on \(\mathbb R^3\). Application to control affine systems on \(\mathbb R^3\) with a scalar input

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