Sub-Finsler Geodesics on the Cartan Group
Ardentov, A. A., Le Donne, E., & Sachkov, Y. L. (2019). Sub-Finsler Geodesics on the Cartan Group. Regular and Chaotic Dynamics, 24(1), 36-60. https://doi.org/10.1134/S1560354719010027
Published inRegular and Chaotic Dynamics
© 2019, Pleiades Publishing, Ltd.
This paper is a continuation of the work by the same authors on the Cartan groupequipped with the sub-Finsler∞norm. We start by giving a detailed presentation of thestructure of bang-bang extremal trajectories. Then we prove upper bounds on the number ofswitchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang,or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove thatevery two points can be connected by a piecewise smooth minimizer, and we give a uniformbound on the number of such pieces.
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Related funder(s)European Commission; Academy of Finland
Funding program(s)Research post as Academy Research Fellow, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingThe work of A. Ardentov and Yu. Sachkov wassupported by the Russian Science Foundation under grant 17-11-01387 and performed at theAilamazyan Program Systems Institute of the Russian Academy of Sciences. E. Le Donne waspartially supported by the Academy of Finland (grant 288501 “Geometry of sub-Riemanniangroups”) and by the European Research Council (ERC Starting Grant 713998 GeoMeG “Geometryof Metric Groups”). ...
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