Geometric approach to Goursat flags
Montgomery, Richard ; Zhitomirskii, Michail
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001), p. 459-493 / Harvested from Numdam
@article{AIHPC_2001__18_4_459_0,
     author = {Montgomery, Richard and Zhitomirskii, Michail},
     title = {Geometric approach to Goursat flags},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {18},
     year = {2001},
     pages = {459-493},
     mrnumber = {1841129},
     zbl = {1013.58004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2001__18_4_459_0}
}
Montgomery, Richard; Zhitomirskii, Michail. Geometric approach to Goursat flags. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) pp. 459-493. http://gdmltest.u-ga.fr/item/AIHPC_2001__18_4_459_0/

[1] Bryant R.L., Chern S.S., Gardner R.B., Goldschmidt H.L., Griffiths P.A., Exterior Differential Systems, Math. Sci. Res. Inst. Publ., 18, Springer-Verlag, 1991. | MR 1083148 | Zbl 0726.58002

[2] Cartan E., Sur certaines expressions différentielles et le problème de Pfaff, Ann. Ec. Normale 16 (1899) 239-332. | JFM 30.0313.04 | Numdam | MR 1508969

[3] Cartan E., Sur l'équivalence absolue de certains systèmes d'équations différentielles et sur certaines familles de courbes, Ann. Ec. Norm. Sup. 42 (1914) 12-48. | JFM 45.1294.04 | Numdam | MR 1504722

[4] Engel F., Zur Invariantentheorie der Systeme von Pfaffschen Gleichungen, Berichte Verhandlungen der Koniglich Sachsischen Gesellschaft der Wissenschaften Mathematisch-Physikalische Klasse 41, 1889. | JFM 21.0340.01

[5] Fliess M., Levine J., Martin P., Rouchon P., On differential flat nonlinear systems, in: Proceedings of the IFAC Nonlinear Control Systems Design Symposium, Bordeaux, 1992, pp. 408-412.

[6] Frobenius F., Uber das Pfaffsche Problem, Journal de Crelle 82 (1887) 230-315. | JFM 09.0249.03

[7] Gaspar M., Sobre la clasificacion de sistemas de Pfaff en bandera (Span.), in: Proc. of the 10th Spanish-Portuguese Conf. on Math., University of Murcia, 1985, pp. 67-74.

[8] Gershkovich V., Exotic Engel structures on R4, Russian J. Math. Phys. 3 (2) (1995) 207-226. | MR 1350504 | Zbl 0909.53022

[9] Giaro A., Kumpera A., Ruiz C., Sur la lecture correcte d'un résultat d'Elie Cartan, C. R. Acad. Sci. Paris 287 (1978) 241-244. | Zbl 0398.58003

[10] Golubev A., On the global stability of maximally nonholonomic two-plane fields in four dimensions, Intern. Math. Res. Notices 11 (1997) 523-529. | MR 1448335 | Zbl 0893.58007

[11] Goursat E., Leçons sur le Problème de Pfaff, Hermann, Paris, 1923. | JFM 48.0538.01

[12] Gray J.W., Some global properties of contact structures, Ann. of Math. 69 (2) (1959) 421-450. | MR 112161 | Zbl 0092.39301

[13] Jean F., The car with n trailers: characterization of the singular configurations, ESIAM: Control, Optimization and Calculus of Variations 1 (1996) 241-266. | Numdam | MR 1411581 | Zbl 0874.93033

[14] Kumpera A., Ruiz C., Sur l'équivalence locale des systèmes de Pfaff en drapeau, in: Gherardelli F. (Ed.), Monge-Ampere Equations and Related Topics, Roma, 1982, pp. 201-248. | MR 704040 | Zbl 0516.58004

[15] Luca F., Risler J.-J., The maximum of the degree of nonholonomy for the car with n trailers, in: Proceedings of the 4th IFAC Symposium on Robot Control, Capri, 1994.

[16] Montgomery R., Engel deformations and contact structures, in: Eliashberg Y., Weinstein A. (Eds.), Amer. Math. Soc. Transl. (2), 196, 1999, pp. 103-117. | MR 1736216 | Zbl 0961.53043

[17] Mormul P., Cheaito M., Rank-2 distributions satisfying the Goursat condition: all their local models in dimension 7 and 8, ESAIM: Control, Optimization and Calculus of Variations 4 (1999) 137-158. | Numdam | MR 1816509 | Zbl 0957.58002

[18] Mormul P., Local classification of rank-2 distributions satisfying the Goursat condition in dimension 9, in: Orro P., Pelletier F. (Eds.), Singularites et Geometrie Sous-Riemannienne, Travaux en Cours, 62, Paris, 2000, pp. 89-119. | Zbl 1141.58302

[19] Mormul P., Contact hamiltonians distinguishing locally certain Goursat systems, in: Poisson Geometry, Banach Center Publications 51, Warsaw, 2000, pp. 219-230. | MR 1764448 | Zbl 0965.37051

[20] Murray R., Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation, Math. Contr. Sign. Sys. 7 (1994) 58-75. | MR 1359021 | Zbl 0825.93319

[21] Sordalen O.J., Conversion of the kinematics of a car with n trailers into a chain form, IEEE International Conference on Robotics and Automation, 1993.

[22] Sordalen O.J., On the global degree of nonholonomy of a car with n trailers, Memorandum of Electronic Research Laboratory, Berkeley, 1993.

[23] Zhitomirskii M., Normal forms of germs of distributions with a fixed growth vector, Leningrad Math. J. 5 (2) (1990) 125-149. | MR 1086448 | Zbl 0732.58004