@article{COCV_1999__4__245_0, author = {Bonnard, Bernard and Chyba, Monique}, title = {M\'ethodes g\'eom\'etriques et analytiques pour \'etudier l'application exponentielle, la sph\`ere et le front d'onde en g\'eom\'etrie sous-riemannienne dans le cas {Martinet}}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {245--334}, publisher = {EDP-Sciences}, volume = {4}, year = {1999}, mrnumber = {1696290}, zbl = {0929.53016}, language = {fr}, url = {http://archive.numdam.org/item/COCV_1999__4__245_0/} }
TY - JOUR AU - Bonnard, Bernard AU - Chyba, Monique TI - Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le cas Martinet JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1999 SP - 245 EP - 334 VL - 4 PB - EDP-Sciences UR - http://archive.numdam.org/item/COCV_1999__4__245_0/ LA - fr ID - COCV_1999__4__245_0 ER -
%0 Journal Article %A Bonnard, Bernard %A Chyba, Monique %T Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le cas Martinet %J ESAIM: Control, Optimisation and Calculus of Variations %D 1999 %P 245-334 %V 4 %I EDP-Sciences %U http://archive.numdam.org/item/COCV_1999__4__245_0/ %G fr %F COCV_1999__4__245_0
Bonnard, Bernard; Chyba, Monique. Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le cas Martinet. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 245-334. http://archive.numdam.org/item/COCV_1999__4__245_0/
[1] Sub-Riemannian sphere in Martinet flat case. ESAIM:COCV 2 ( 1997) 377-448. | EuDML | Numdam | MR | Zbl
, , and[2] Sub-Riemannian metrics on R3. Geometric Control and Non-holonomic Problems in Mechanics, Conference Proceedings Series, Canad. Math. Soc. (to appear). | Zbl
, and ,[3] Exponentional representations of flows and chronological calculus. Math. USSR Sb. 35 ( 1979) 727-785. | Zbl
and ,[4] Strong minimality of abnormal geodesics for 2- distributions. J. Dynamical and Control Systems 1 ( 1995). 139-176. | MR | Zbl
and ,[5] Abnormal geodesics in SR-geometry subanalycity. Preprint ( 1997). | MR
and ,[6] Theory of oscillations, Dover, New-York ( 1966). | Zbl
, and ,[7] Non-integrable geodesics in SR-Martinet geometry, Proceedings AMS conference, Boulder ( 1997). | Zbl
, and ,[8] Sub-Riemannian geometry: one parameter deformation of the Martinet flat case. J. Dynamical and Control Systems 4 ( 1998) 59-76. | MR | Zbl
, and ,[9] The transcendence we need to compute the Sphere and the Wave Front in Martinet SR-Geometry. to appear in Proc. of Steklov Institute. | Zbl
, and ,[10] The role of abnormal minimizers in SR-geometry. Preprint ( 1999). | Numdam | MR | Zbl
and ,[11] Le cas Martinet en géométrie sous-Riemannienne, Thèse de l'Université de Bourgogne ( 1997).
,[12] Introduction to non linear differential and integral equations, Dover, New-York, ( 1962). | Zbl
,[13] Calcul infinitésimal, Hermann, Paris ( 1980). | MR | Zbl
,[14] The elementary theory of restricted analytic fields with exponentiation, Annals of Mathematics 140 ( 1994) 183-205. | MR | Zbl
, and ,[15] Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac, Hermann, Paris ( 1992). | MR | Zbl
,[16] Traité des fonctions elliptiques, Gauthier-Villars, Tomes I à IV, Paris ( 1886).
,[17] Distance sous-riemannienne et sous analycité.Preprint ( 1997).
,[18] Fewnomials, Trans. Math. Monographs 88, ( 1991). | Zbl
,[19] Abnormal extremals. Preprint ( 1992).
,[20] Géométrie sous-Riemannienne, Séminaire Bourbaki ( 1996). | EuDML | Numdam | MR | Zbl
,[21] Elliptic functions and applications, Springer-Verlag, New-York ( 1989). | MR | Zbl
,[22] Foundations of optimal control theory, John Wiley and Sons, New-York ( 1967). | MR | Zbl
and ,[23] Differential equations: geometry theory, Dover, New-York ( 1977).
,[24] Problème général de la stabilité du mouvement. Annals of Maths. Studies, Princeton University Press ( 1947). | MR | Zbl
,[25] Théorèmes de préparation pour les fonctions logarithmo-exponentielles. Annales de l'Institut Fourier 47 ( 1997) 859- 884. | EuDML | Numdam | MR | Zbl
and ,[26] Shortest paths for sub-Riemannian metrics of rank-2 distributions. Memoirs of the Americain Math. Society 118, ( 1995). | Zbl
and ,[27] Some examples of reachable sets and optimal cost functions that fail to be subanalytic. SIAM J. Control Optim. 23 ( 1985) 584-598. | MR | Zbl
and ,[28] A treatise of the mathematical theory of elasticity, Dover ( 1944). | JFM | MR | Zbl
,[29] Abnormal minimizers, SIAM J. Control Optim. 32 ( 1994) 1605-1620. | MR | Zbl
,[30] Applications de Dulac et applications pfaffiennes. Bulletin SMF 125 ( 1997) 1-13. | EuDML | Numdam | MR | Zbl
and ,[31] Théorie de Khovanski et problème de Dulac. Inv. Math. 105 ( 1991) 431-441. | EuDML | MR | Zbl
and ,[32] Bifurcations of planar vector fields and Hilbert's 16th problem, Birkhauser, Berlin ( 1998). | Zbl
,[33] Nonlinear elasticity, Gordon and Breach, London ( 1968). | MR | Zbl
,[34] Nonlinear differential equations, Mac Graw Hill ( 1962). | Zbl
,[35] Éléments de la théorie des fonctions elliptiques, Gauthier-Villars, Tomes I à IV, Paris ( 1896). | JFM
and ,[36] A course of modem analysis, Cambridge U. Press, New York ( 1927). | JFM
and ,