[go: up one dir, main page]
no. 4
Geometric approach to Goursat flags
Montgomery, Richard ; Zhitomirskii, Michail1
1 Technion, Department of Mathematics, 32000 Haifa (Israël)
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 4, pp. 459-493.
Montgomery, Richard  ; Zhitomirskii, Michail 1

1 Technion, Department of Mathematics, 32000 Haifa (Israël) 
@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},
     pages = {459--493},
     publisher = {Elsevier},
     volume = {18},
     number = {4},
     year = {2001},
     mrnumber = {1841129},
     zbl = {1013.58004},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2001__18_4_459_0/}
}
TY  - JOUR
AU  - Montgomery, Richard
AU  - Zhitomirskii, Michail
TI  - Geometric approach to Goursat flags
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2001
SP  - 459
EP  - 493
VL  - 18
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/item/AIHPC_2001__18_4_459_0/
LA  - en
ID  - AIHPC_2001__18_4_459_0
ER  - 
%0 Journal Article
%A Montgomery, Richard
%A Zhitomirskii, Michail
%T Geometric approach to Goursat flags
%J Annales de l'I.H.P. Analyse non linéaire
%D 2001
%P 459-493
%V 18
%N 4
%I Elsevier
%U http://www.numdam.org/item/AIHPC_2001__18_4_459_0/
%G en
%F 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) no. 4, pp. 459-493. http://www.numdam.org/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 | Zbl

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

[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 | Numdam | MR

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

[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

[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 | Zbl

[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

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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. | EuDML | Numdam | MR | Zbl

[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

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

[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 | Zbl

[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 | Zbl