Abstract
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler ℓ∞ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings 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 that every two points can be connected by a piecewise smooth minimizer, and we give a uniform bound on the number of such pieces.
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Ardentov, A., Le Donne, E., and Sachkov, Yu., A Sub-Finsler Problem on the Cartan Group, Tr. Mat. Inst. Steklova, 2019, accepted.
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Ardentov, A.A., Le Donne, E. & Sachkov, Y.L. Sub-Finsler Geodesics on the Cartan Group. Regul. Chaot. Dyn. 24, 36–60 (2019). https://doi.org/10.1134/S1560354719010027
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DOI: https://doi.org/10.1134/S1560354719010027