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Sub-Lorentzian extremals defined by an antinorm
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We consider a left-invariant (sub-)Lorentzian structure on a Lie group. We assume that this structure is defined by a closed convex salient cone in the corresponding Lie algebra and a continuous antinorm associated with this cone. We derive the Hamiltonian system for (sub-)Lorentzian extremals and give conditions under that normal extremal trajectories keep their causal type. Tangent vectors of abnormal extremal trajectories are either light-like or tangent vectors of sub-Riemannian extremal trajectories for the sub-Riemannian distribution spanned by the cone.
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Explicit formulas for extremals in sub-Lorentzian and Finsler problems on 2- and 3-dimensional Lie groups
New functions cosh_Ω and sinh_Ω are introduced, and explicit formulas for sub-Lorentzian and Finsler extremals on 3D unimodular Lie groups and the Lobachevsky plane are derived.
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