Sub-Finsler geodesics on the Cartan group

DOI10.1134/S1560354719010027zbMath1412.49084arXiv1810.05431OpenAlexW2896888818WikidataQ109520608 ScholiaQ109520608MaRDI QIDQ1739580

Andrei A. Ardentov, Yuri L. Sachkov, Enrico Le Donne

Publication date: 26 April 2019

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.05431

zbMATH Keywords

time-optimal controlgeometric controlsub-Finsler geometryCartan groupbang-bang minimizers

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30) Geodesics in global differential geometry (53C22) Optimality conditions for problems involving ordinary differential equations (49K15) Sub-Riemannian geometry (53C17)

Related Items

Multiexponential maps in Carnot groups with applications to convexity and differentiability ⋮ Periodic controls in step 2 strictly convex sub-Finsler problems ⋮ Pansu-Wulff shapes in \(\mathbb{H}^1\) ⋮ Coadjoint orbits and time-optimal problems for step-2 free nilpotent Lie groups ⋮ Casimir functions of free nilpotent Lie groups of steps 3 and 4 ⋮ Periodic time-optimal controls on two-step free-nilpotent Lie groups ⋮ Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2 ⋮ The isoperimetric problem for regular and crystalline norms in \({\mathbb{H}}^1\)

Cites Work

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• Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy
• Sub-Finsler geometry in dimension three
• Structure of homogeneous locally compact spaces with intrinsic metric
• Geometry of sub-Finsler Engel manifolds
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Homogeneous manifolds with intrinsic metric. II
• Control theory from the geometric viewpoint.
• A sub-Finsler problem on the Cartan group
• Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions
• Sub-Finslerian Metric Associated to an Optimal Control System
• Exponential map in the generalized Dido problem
• Sub-Finsler Geometry and Finite Propagation Speed
• On the rate of convergence to the asymptotic cone for nilpotent groups and subFinsler geometry
• A metric characterization of Carnot groups
• Blowups and blowdowns of geodesics in Carnot groups