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Journal of Dynamical and Control Systems

, Volume 1, Issue 2, pp 139–176 | Cite as

Strong minimality of abnormal geodesics for 2-distributions

  • A. A. Agrachev
  • A. V. Sarychev
Article

Abstract

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 

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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

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