Andrei A. Ardentov, Enrico Le Donne, Yuri L. Sachkov, “Sub-Finsler Geodesics on the Cartan Group”, Regul. Chaotic Dyn., 24:1 (2019), 36–60
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.