Small sub-riemannian balls on R3

Journal of Dynamical and Control Systems

Volumn 2, Issue 3, 1996, Pages 359-421

  El Alaoui, El H Ch ^a  

^a UNIVERSITÉ ET INSA DE ROUEN   (France)

Author keywords

Conjugate locus; Contact structure; Differential invariant; Normal form; Sub Riemannian geometry

Indexed keywords

CONFORMAL MAPPING; INVARIANCE; MATHEMATICAL MODELS; POLES AND ZEROS; ROOT LOCI; SET THEORY;

CONJUGATE LOCUS; CONTACT STRUCTURE; DIFFERENTIAL INVARIANT; NORMAL FORM; SUB-RIEMANNIAN GEOMETRY;

GEOMETRY;

EID: 0030195721     PISSN: 10792724     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02269424     Document Type: Article

References (25)

1. A. Agrachev, Methods of control theory in nonholonomic geometry. Proc. ICM-94, Birkhäuser, Zürich, 1995.
2. 3. Comptes-Rendus à l'Académie Sci., Paris, 1996, 377-384.
3. V. Arnold, A. Varchenko, and S. Goussein-Zade, Singularités des applications différentiables. (French translation) Mir, Moscow, 1986.
4. R. W. Brockett, Control theory and singular Riemannian geometry. In: New Directions in Appl. Math., P. J. Hilton and G. S. Young, Eds, Springer Verlag, 1981.
5. O. Endler, Valuation theory, Springer Verlag, Universitext, 1972.
6. E. Falbel and C. Gorodski, Sub-Riemannian homogeneous spaces in dimension 3 and 4. Preprint, Instituto de Mathematica e Estatistica, Universidade de Sao Paolo, 1994.
7. Z. Ge, On the cut points and conjugate points in a constrained variational problem. Fields Inst. Commun. 1 (1993), 113-132.
8. M. Gromov, Carnot-Caratheodory spaces seen from within. Preprint IHES, Feb. 1994.
9. S. Helgason, Differential geometry and symmetric spaces. Academic Press, New York, 1962.
10. I. Kupka, Abnormal extremals. Preprint, 1992.
11. W. Liu and H. J. Sussmann, Abnormal Sub-Riemannian minimizers. In: Differ. Equations, Dynamical Systems and Control Science, K. D. Elworthy, W. N. Everitt, and E. B. Lee, Eds, Lect. Notes Pure Appl. Math. Vol. 152, M. Dekker, New York, 1993, 705-716.
12. _, Shortest paths for sub-Riemannian metrics on rank-2 distributions (to appear).
13. ∞ mappings. I-VI. Ann. Math. 87 (1968), 89-104;
14. 89 (1969), 254-291;
15. Publ. Sci. IHES 35 (1969), 127-156;
16. 37 (1970), 223-248;
17. Adv. Math. 4 (1970), 301-335;
18. Lect. Notes Math. 192 (1971), 207-253.
19. R. Montgomery, Abnormal minimizers. SIAM J. Control and Optimiz. 32 (1994), No. 6, 1605-1620.
20. L. S. Pontryagin, V. G. Boltianskii, R. V. Gamkrelidze, and E. F. Mischednko, La théorie mathématique des processus optimaux. (French translation) Mir, Moscow, 1974.
21. M. Rumin, Formes différentielles sur les variétés de contact. PHD Thesis, Univ. of Paris Sud., 1992.
22. R. S. Strichartz, Sub-Riemannian geometry. J. Differ. Geom. 24 (1986), 221-263.
23. A. M. Vershik and V. Y. Gershkovich, Nonholonomic geometry and nilpotent analysis. J. Geom. and Phys. 53 (1989), 407-452.
24. _, The geometry of the nonholonomic sphere for three-dimensional Lie groups. In: Encyclopedia Math. Sci. 16, Dynamical Systems 7, Springer-Verlag, 1994.
25. H. Whitney, On singularities of mapping of Euclidean spaces. Ann. Math. 62 (1955), No. 3.