Journal of Dynamical and Control Systems

, Volume 21, Issue 2, pp 155–171 | Cite as

Duality of Singular Paths for (2, 3, 5)-Distributions

  • Goo IshikawaEmail author
  • Yumiko Kitagawa
  • Wataru Yukuno


We show a duality which arises from distributions of Cartan type, having growth (2, 3, 5), from the viewpoint of geometric control theory. In fact, we consider the space of singular (or abnormal) paths on a given five-dimensional space endowed with a Cartan distribution, which form another five-dimensional space with a cone structure. We regard the cone structure as a control system and show that the space of singular paths of the cone structure is naturally identified with the original space. Moreover, we observe an asymmetry on this duality in terms of singular paths.


Singular control Cartan prolongation Cone structure 

Mathematics Subject Classifications (2010)

58A30 53A55 53C17 



This work was supported by KAKENHI no. 22340030 and no. 23654058.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan
  2. 2.Oita National College of TechnologyOitaJapan

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