Journal of Dynamical and Control Systems

, Volume 1, Issue 2, pp 139–176

Strong minimality of abnormal geodesics for 2-distributions

  • A. A. Agrachev
  • A. V. Sarychev


We investigate the local length minimality (by theW1,1- orH1-topology) of abnormal sub-Riemannian geodesics for rank 2 distributions. In particular, we demonstrate that this kind of local minimality is equivalent to the rigidity for generic abnormal geodesics, and introduce an appropriateJacobi equation in order to computeconjugate points. As a corollary, we obtain a recent result of Sussmann and Liu about the global length minimality of short pieces of the abnormal geodesics.

1991 Mathematics Subject Classification

49K30 53C22 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • A. A. Agrachev
    • 1
  • A. V. Sarychev
    • 2
  1. 1.Steklov Mathematics InstituteMoscowRussia
  2. 2.Departament of MathematicsUniversity of AveiroAveiroPortugal

Personalised recommendations