Geometric approach to Goursat flags
Richard Montgomery; Michail Zhitomirskii[1]
- [1] Technion, Department of Mathematics, 32000 Haifa (Israël)
Annales de l'I.H.P. Analyse non linéaire (2001)
- Volume: 18, Issue: 4, page 459-493
- ISSN: 0294-1449
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topMontgomery, Richard, and Zhitomirskii, Michail. "Geometric approach to Goursat flags." Annales de l'I.H.P. Analyse non linéaire 18.4 (2001): 459-493. <http://eudml.org/doc/78528>.
@article{Montgomery2001,
affiliation = {Technion, Department of Mathematics, 32000 Haifa (Israël)},
author = {Montgomery, Richard, Zhitomirskii, Michail},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {distribution; Cartan prolongation; Goursat flag; Goursat singularity},
language = {eng},
number = {4},
pages = {459-493},
publisher = {Elsevier},
title = {Geometric approach to Goursat flags},
url = {http://eudml.org/doc/78528},
volume = {18},
year = {2001},
}
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
PB - Elsevier
VL - 18
IS - 4
SP - 459
EP - 493
LA - eng
KW - distribution; Cartan prolongation; Goursat flag; Goursat singularity
UR - http://eudml.org/doc/78528
ER -
References
top- [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. Zbl0726.58002MR1083148
- [2] Cartan E., Sur certaines expressions différentielles et le problème de Pfaff, Ann. Ec. Normale16 (1899) 239-332. Zbl30.0313.04MR1508969JFM30.0313.04
- [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. Zbl45.0472.04MR1504722JFM45.1294.04
- [4] Engel F., Zur Invariantentheorie der Systeme von Pfaffschen Gleichungen, Berichte Verhandlungen der Koniglich Sachsischen Gesellschaft der Wissenschaften Mathematisch-Physikalische Klasse 41, 1889. JFM21.0340.01
- [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 Crelle82 (1887) 230-315. JFM09.0249.03
- [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. Zbl0909.53022MR1350504
- [9] Giaro A., Kumpera A., Ruiz C., Sur la lecture correcte d'un résultat d'Elie Cartan, C. R. Acad. Sci. Paris287 (1978) 241-244. Zbl0398.58003
- [10] Golubev A., On the global stability of maximally nonholonomic two-plane fields in four dimensions, Intern. Math. Res. Notices11 (1997) 523-529. Zbl0893.58007MR1448335
- [11] Goursat E., Leçons sur le Problème de Pfaff, Hermann, Paris, 1923. JFM48.0538.01
- [12] Gray J.W., Some global properties of contact structures, Ann. of Math.69 (2) (1959) 421-450. Zbl0092.39301MR112161
- [13] Jean F., The car with n trailers: characterization of the singular configurations, ESIAM: Control, Optimization and Calculus of Variations1 (1996) 241-266. Zbl0874.93033MR1411581
- [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. Zbl0516.58004
- [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. Zbl0961.53043MR1736216
- [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 Variations4 (1999) 137-158. Zbl0957.58002MR1816509
- [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.
- [19] Mormul P., Contact hamiltonians distinguishing locally certain Goursat systems, in: Poisson Geometry, Banach Center Publications 51, Warsaw, 2000, pp. 219-230. Zbl0965.37051MR1764448
- [20] Murray R., Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation, Math. Contr. Sign. Sys.7 (1994) 58-75. Zbl0825.93319MR1359021
- [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. MR1086448
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