Regular and Chaotic Dynamics

, Volume 24, Issue 1, pp 36–60 | Cite as

Sub-Finsler Geodesics on the Cartan Group

  • Andrei A. ArdentovEmail author
  • Enrico Le Donne
  • Yuri L. Sachkov


This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler 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.


Sub-Finsler geometry time-optimal control geometric control Cartan group 

MSC2010 numbers:

49J15 49K15 


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • Andrei A. Ardentov
    • 1
    Email author
  • Enrico Le Donne
    • 2
  • Yuri L. Sachkov
    • 1
  1. 1.Program Systems Institute of RASPereslavl-Zalessky, Yaroslavl RegionRussia
  2. 2.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland

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