Characteristic vector fields of generic distributions of corank 2

B. Jakubczyk; W. Kryński; F. Pelletier

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 1, page 23-38
  • ISSN: 0294-1449

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Jakubczyk, B., Kryński, W., and Pelletier, F.. "Characteristic vector fields of generic distributions of corank 2." Annales de l'I.H.P. Analyse non linéaire 26.1 (2009): 23-38. <http://eudml.org/doc/78838>.

@article{Jakubczyk2009,
author = {Jakubczyk, B., Kryński, W., Pelletier, F.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {tangent distributions; generic distributions; singular curves; abnormal curves; characteristic vector fields},
language = {eng},
number = {1},
pages = {23-38},
publisher = {Elsevier},
title = {Characteristic vector fields of generic distributions of corank 2},
url = {http://eudml.org/doc/78838},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Jakubczyk, B.
AU - Kryński, W.
AU - Pelletier, F.
TI - Characteristic vector fields of generic distributions of corank 2
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 1
SP - 23
EP - 38
LA - eng
KW - tangent distributions; generic distributions; singular curves; abnormal curves; characteristic vector fields
UR - http://eudml.org/doc/78838
ER -

References

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  1. [1] Agrachev A., Methods of control theory in nonholonomic geometry, in: Zurich 1994, Proc. Int. Congress of Math., vol. 2, Birkhäuser, Basel, 1995, pp. 1473-1483. Zbl0848.93012MR1404051
  2. [2] Agrachev A., Sarychev A., Abnormal sub-Riemannian geodesics: Morse index and rigidity, Ann. Inst. H. Poincaré, Anal. Non Lineaire13 (6) (1996) 635-690. Zbl0866.58023MR1420493
  3. [3] Bismut J.M., Large Deviations and the Malliavin Calculus, Birkhäuser, 1984. Zbl0537.35003MR755001
  4. [4] Bryant R.L., Hsu L., Rigidity of integral curves of rank 2 distributions, Invent. Math.114 (1993) 435-461. Zbl0807.58007MR1240644
  5. [5] Chitour Y., Jean F., Trélat E., Genericity results for singular curves, J. Differential Geom.73 (2006) 45-73. Zbl1102.53019MR2217519
  6. [6] Jakubczyk B., Przytycki F., Singularities of k-tuples of vector fields, Dissertationes Math.213 (1984) 1-64, Warsaw. Zbl0565.58007MR744876
  7. [7] Jakubczyk B., Zhitomirskii M., Distributions of corank 1 and their characteristic vector fields, Trans. Am. Math. Soc.355 (2003) 2857-2883. Zbl1022.58002MR1975403
  8. [8] Kryński W., Singular curves determine generic distributions of corank at least 3, J. Dynamical Control Syst.11 (3) (2005) 375-388. Zbl1088.58003MR2147191
  9. [9] Liu W., Sussmann H., Shortest paths for sub-Riemannian metrics on rank 2 distributions, Mem. Amer. Math. Soc.118 (564) (1995). Zbl0843.53038MR1303093
  10. [10] Montgomery R., Abnormal minimizers, SIAM J. Control Optim. (1994). Zbl0816.49019MR1297101
  11. [11] Montgomery R., A survey on singular curves in sub-Riemannian geometry, J. Dynam. Control Syst.1 (1) (1995) 49-90. Zbl0941.53021MR1319057
  12. [12] Pelletier F., Singularités génériques des distributions de codimension 2 et structures bihamiltoniennes, Bull. Sci. Math.125 (3) (2001) 197-234. Zbl1183.49004MR1822688
  13. [13] Rayner C.B., The exponential map for the Lagrange problem on differentiable manifolds, Philos. Trans. R. Soc. London. Ser. A Math. Phys. Sci.262 (1127) (1967) 299-344. Zbl0154.37004MR247552
  14. [14] Sussmann H.J., An introduction to the coordinate-free maximum principle, in: Jakubczyk B., Respondek W. (Eds.), Geometry of Feedback and Optimal Control, Pure and Applied Math., vol. 207, Marcel Dekker, New York, 1998, pp. 463-557. Zbl0925.93135MR1493021
  15. [15] Ślebodziński W., Formes extérieures et leurs applications, Monografie Matematyczne, vol. 31, Polish Scientific Publishers, Warszawa, 1954. Zbl0057.13204
  16. [16] Vershik A.M., Gershkovitch V.Ya., An estimate of functional dimension for orbits of germs of generic distributions, Matem. Zametki44 (1988) 596-603. Zbl0667.58003
  17. [17] Zhitomirskii M., Typical Singularities of Differential 1-Forms and Pfaffian Equations, Translations of Math. Monographs, vol. 113, AMS, Providence, 1992. Zbl0771.58001MR1195792

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