@article{COCV_1997__2__377_0, author = {Agrachev, A. and Bonnard, B. and Chyba, M. and Kupka, I.}, title = {Sub-riemannian sphere in {Martinet} flat case}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {377--448}, publisher = {EDP-Sciences}, volume = {2}, year = {1997}, mrnumber = {1483765}, zbl = {0902.53033}, language = {en}, url = {http://www.numdam.org/item/COCV_1997__2__377_0/} }
TY - JOUR AU - Agrachev, A. AU - Bonnard, B. AU - Chyba, M. AU - Kupka, I. TI - Sub-riemannian sphere in Martinet flat case JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1997 SP - 377 EP - 448 VL - 2 PB - EDP-Sciences UR - http://www.numdam.org/item/COCV_1997__2__377_0/ LA - en ID - COCV_1997__2__377_0 ER -
%0 Journal Article %A Agrachev, A. %A Bonnard, B. %A Chyba, M. %A Kupka, I. %T Sub-riemannian sphere in Martinet flat case %J ESAIM: Control, Optimisation and Calculus of Variations %D 1997 %P 377-448 %V 2 %I EDP-Sciences %U http://www.numdam.org/item/COCV_1997__2__377_0/ %G en %F COCV_1997__2__377_0
Agrachev, A.; Bonnard, B.; Chyba, M.; Kupka, I. Sub-riemannian sphere in Martinet flat case. ESAIM: Control, Optimisation and Calculus of Variations, Volume 2 (1997), pp. 377-448. http://www.numdam.org/item/COCV_1997__2__377_0/
[1] Strong minimality of abnormal geodesics for 2-distributions, Journal of Dynamical and control Systems, 2, 1995, 139-176. | MR | Zbl
, :[2] Exponential mappings for contact sub-Riemannian structures, Journal of dynamical and Control Systems, 2, 1996, 321-358. | MR | Zbl
:[3] Any smooth simple H1-local length minimizer in the Carnot-Caratheodory space is a C0-local minimizer, Preprint of Laboratoire de Topologie, Dijon, 1996.
:[4] Méthodes mathématiques pour la mécanique classique, Éditions MIR, Moscou, 1976. | MR | Zbl
:[5] Lectures on the calculus of variations, The University of Chicago Press, 1946. | MR | Zbl
:[6] Feedback equivalence for nonlinear systems and the time optimal control problem, SIAM J. on Control and Opt., 29, 1991, 1300-1321. | MR | Zbl
:[7] Exponential mapping, sphere and waves front in SR-geometry: the generic integrable Martinet case, Preprint of Laboratoire de Topologie, Dijon, 1997.
, :[8] Contrôle optimal géométrique appliqué, Preprint of Laboratoire de Topologie, Dijon, 1995.
, , :[9] Non-integrable geodesics in SR Martinet geometry, in Proceedings AMS conference, Boulder, 1997. | Zbl
, , :[10] Sub-Riemannian geometry: one parameter deformation of the Martinet flat case, to appear in Journal of Dynamical and Control Systems. | MR | Zbl
, , :[11] Control theory and singular Riemannian geometry, in New directions in applied Math., Springer-Verlag, New-York, 1981. | MR | Zbl
:[12] Leçons sur la géométrie des espaces de Riemann, Ed. J. Gabay, Paris, 1988. | MR | Zbl
:[13] Introduction to non linear differential and integral equation, Dover, New-York, 1962. | Zbl
:[14] Calcul Infinitésimal, Hermann, Paris, 1980. | MR | Zbl
:[15] Riemannian geometry, Birkhauser, Boston, 1992. | MR | Zbl
:[16] The elementary theory of restricted analytic fields with exponentiation, Annals of Mathematics, 140, 1994, 183-205. | MR | Zbl
, , :[17] Small sub-Riemannian balls on R3, Journal of dynamical and Control Systems, 2, 1996, 359-421. | MR | Zbl
, , :[18] Singular nonlinear PDE, Vieweg-Verlag, Germany, 1996.
, :[19] Quadratic form theory and differential equation, Academic Press, New-York, 1980. | MR | Zbl
:[20] Some regularity theorem for Carnot-Caratheodory metries, J. Differential geometry, 32, 1991, 819-850. | MR | Zbl
:[21] Partial differential equations, Springer-Verlag, New-York, 1971. | Zbl
:[22] Fewnomials, Trans. AMS, 88, 1991. | MR | Zbl
:[23] Abnormal extremals, Preprint, 1992.
:[24] Géométrie sous-Riemannienne, in Séminaire Bourbaki, 1996. | Numdam | MR
:[25] Elliptic functions and applications, Springer-Verlag, New-York, 1989. | MR | Zbl
:[26] Foundations of optimal control theory, John Wiley and Sons, New-York, 1967. | MR | Zbl
, :[27] Théorèmes de préparation pour les fonctions logarithmo-exponentielles, Annales de l'Institut Fourier, 47, 1997, 859-884. | Numdam | MR | Zbl
, :[28] Shortest paths for sub-Riemannian metries of rank two distributions, to appear in Trans. AMS. | Zbl
and :[29] Some examples of reachable sets and optimal cost functions that fail to be subanalytic, SIAM J. Control and Optimization, 23, 1985, 584-598. | MR | Zbl
, :[30] A treatise of the mathematical theory of elasticity, Dover, 1944. | JFM | MR | Zbl
:[31] Connections between differential geometry and topology, Duke Math. J., 1, 1935, 376-391. | JFM | MR
:[32] Théorie mathématique des processus optimaux, Éditions MIR, Moscou, 1974. | MR | Zbl
et al.:[33] Feedback classification of nonlinear control Systems on 3-manifolds, to appear in Math. Control Systems and Signals. | MR | Zbl
, :[34] Differential geometry, Publish on Perish, Inc., Berkeley, 1979.
:[35] Sub-Riemannian geometry, J. Differential geometry, 24, 1986, 221-263. | MR | Zbl
:[36] Eléments de la théorie des fonctions elliptiques, Tomes I à IV, Gauthier-Villars, Paris, 1896. | JFM
, :[37] The cut-locus and conjugate-locus of a Riemannian manifold, Annals of Maths, 87, 1968, 29-41. | MR | Zbl
:[38] A course of modern analysis, Cambridge U. Press, New York, 1927. | JFM | MR
, :