Characteristic Vector Fields of Generic Distributions of Corank 2
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 1, pp. 23-38. 
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     author = {Jakubczyk, B. and Kry\'nSki, W. and Pelletier, F.},
     title = {Characteristic {Vector} {Fields} of {Generic} {Distributions} of {Corank} 2},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {23--38},
     publisher = {Elsevier},
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     zbl = {1154.53018},
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}
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Jakubczyk, B.; KryńSki, W.; Pelletier, F. Characteristic Vector Fields of Generic Distributions of Corank 2. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 1, pp. 23-38. doi : 10.1016/j.anihpc.2007.05.006. http://www.numdam.org/articles/10.1016/j.anihpc.2007.05.006/

[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. | MR | Zbl

[2] Agrachev A., Sarychev A., Abnormal Sub-Riemannian Geodesics: Morse Index and Rigidity, Ann. Inst. H. Poincaré, Anal. Non Lineaire 13 (6) (1996) 635-690. | Numdam | MR | Zbl

[3] Bismut J. M., Large Deviations and the Malliavin Calculus, Birkhäuser, 1984. | MR | Zbl

[4] Bryant R. L., Hsu L., Rigidity of Integral Curves of Rank 2 Distributions, Invent. Math. 114 (1993) 435-461. | MR | Zbl

[5] Chitour Y., Jean F., Trélat E., Genericity Results for Singular Curves, J. Differential Geom. 73 (2006) 45-73. | MR | Zbl

[6] Jakubczyk B., Przytycki F., Singularities of K-Tuples of Vector Fields, Dissertationes Math. 213 (1984) 1-64, Warsaw. | MR | Zbl

[7] Jakubczyk B., Zhitomirskii M., Distributions of Corank 1 and Their Characteristic Vector Fields, Trans. Am. Math. Soc. 355 (2003) 2857-2883. | MR | Zbl

[8] Kryński W., Singular Curves Determine Generic Distributions of Corank at Least 3, J. Dynamical Control Syst. 11 (3) (2005) 375-388. | MR | Zbl

[9] Liu W., Sussmann H., Shortest Paths for Sub-Riemannian Metrics on Rank 2 Distributions, Mem. Amer. Math. Soc. 118 (564) (1995). | MR | Zbl

[10] Montgomery R., Abnormal Minimizers, SIAM J. Control Optim. (1994). | MR | Zbl

[11] Montgomery R., A Survey on Singular Curves in Sub-Riemannian Geometry, J. Dynam. Control Syst. 1 (1) (1995) 49-90. | MR | Zbl

[12] Pelletier F., Singularités Génériques Des Distributions De Codimension 2 Et Structures Bihamiltoniennes, Bull. Sci. Math. 125 (3) (2001) 197-234. | MR

[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. | MR | Zbl

[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. | MR | Zbl

[15] Ślebodziński W., Formes Extérieures Et Leurs Applications, Monografie Matematyczne, vol. 31, Polish Scientific Publishers, Warszawa, 1954. | Zbl

[16] Vershik A. M., Gershkovitch V. Ya., An Estimate of Functional Dimension for Orbits of Germs of Generic Distributions, Matem. Zametki 44 (1988) 596-603. | Zbl

[17] Zhitomirskii M., Typical Singularities of Differential 1-Forms and Pfaffian Equations, Translations of Math. Monographs, vol. 113, AMS, Providence, 1992. | MR | Zbl

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