@article{AIHPC_1996__13_6_635_0,
author = {Agrachev, A. A. and Sarychev, A. V.},
title = {Abnormal sub-riemannian geodesics : {Morse} index and rigidity},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {635--690},
year = {1996},
publisher = {Gauthier-Villars},
volume = {13},
number = {6},
mrnumber = {1420493},
zbl = {0866.58023},
language = {en},
url = {https://www.numdam.org/item/AIHPC_1996__13_6_635_0/}
}
TY - JOUR AU - Agrachev, A. A. AU - Sarychev, A. V. TI - Abnormal sub-riemannian geodesics : Morse index and rigidity JO - Annales de l'I.H.P. Analyse non linéaire PY - 1996 SP - 635 EP - 690 VL - 13 IS - 6 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPC_1996__13_6_635_0/ LA - en ID - AIHPC_1996__13_6_635_0 ER -
%0 Journal Article %A Agrachev, A. A. %A Sarychev, A. V. %T Abnormal sub-riemannian geodesics : Morse index and rigidity %J Annales de l'I.H.P. Analyse non linéaire %D 1996 %P 635-690 %V 13 %N 6 %I Gauthier-Villars %U https://www.numdam.org/item/AIHPC_1996__13_6_635_0/ %G en %F AIHPC_1996__13_6_635_0
Agrachev, A. A.; Sarychev, A. V. Abnormal sub-riemannian geodesics : Morse index and rigidity. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 6, pp. 635-690. https://www.numdam.org/item/AIHPC_1996__13_6_635_0/
[1] , Quadratic Mappings in Geometric Control Theory, in: Itogi Nauki i Tekhniki; Problemy Geometrii, VINITI, Acad. Nauk SSSR, Moscow, Vol. 20, pp. 11-205, 1988. English transl. in J. Soviet Math., Vol. 51, 1990, pp. 2667-2734. | MR
[2] , Topology of Quadratic Mappings and Hessians of Smooth Mappings, in: Itogi Nauki i Tekhniki; Algebra, Topologia, Geometria; VINITI, Acad. Nauk SSSR, Vol. 26, 1988, pp. 85-124. | Zbl | MR
[3] , The Second-Order Optimality Condition in the General Nonlinear Case, Matem Sbornik, Vol. 102, 1977, pp. 551-568. English transl. in: Math. USSR Sbornik, Vol. 31, 1977. | Zbl | MR
[4] and , Second-Order Optimality Condition for the Time-Optimal Problem, Matem. Sbornik, Vol. 100, 1976, pp. 610-643. English transl. in: Math. USSR Sbornik, Vol. 29, 1976, pp. 547-576. | Zbl | MR
[5] and , Exponential Representation of Flows and Chronological Calculus, Matem. Sbornik, Vol. 107, 1978, pp. 467-532. English transl. in: Math. USSR Sbornik, Vol. 35, 1979, pp. 727-785. | Zbl | MR
[6] , and , Local Invariants of Smooth Control Systems, Acta Applicandae Mathematicae, Vol. 14, 1989, pp. 191-237. | Zbl | MR
[7] and , On Abnormal Extremals for Lagrange Variational Problems, to appear in J. Mathematical Systems, Estimation and Control. | Zbl
[8] and , On Abnormal Extremals for Lagrange Variational Problems (summary), J. Mathematical Systems, Estimation and Control, Vol. 5, 1995, pp. 127-130. | Zbl
[9] , Mathematical Methods of Classical Mechanics, Springer-Verlag, New York-Berlin, 1978. | Zbl | MR
[10] , and , Singularities of Differentiable Mappings, Vol. 1, Birkhäuser, Boston, 1985. | MR
[11] and , Théorie de singularités de l'application entree/sortie et optimalité des trajectoires singulières dans le problème du temps minimal, Preprint, 1990.
[12] , Engel Structures on Four Dimensional Manifolds, University of Melbourne, Department of Mathematics, Preprint Series No. 10, 1992.
[13] , Necessary Conditions for Singular Extremals Involving Multiple Control Variables, SIAM J. Control, Vol. 4, 1966, pp. 716-731. | Zbl | MR
[14] and , Geometric Asymptotics, Amer. Math. Soc., Providence, Rhode Island, 1977. | Zbl | MR
[15] and , Nonlinear Controllability via Lie Theory, SIAM J. on Control, Vol. 8, 1970, pp. 450-460. | Zbl | MR
[16] , and , Singular Extremals, in: G. Leitman Ed., Topics in Optimization, Academic Press, New York, N. Y., 1967, pp. 63-101. | MR
[17] , The High-Order Maximum Principle and its Applications to Singular Extremals, SIAM J. on Control and Optimiz., Vol. 15, 1977, pp. 256-293. | Zbl | MR
[18] and , The Weyl Representation, Maslov Index and Theta-series, Birkhäuser, Boston, 1980. | Zbl | MR
[19] , Geodesics, Which Do Not Satisfy Geodesic Equations, Preprint, 1991.
[20] , The Calculus of variations in the large, Amer. Math. Soc., New York, NY, 1934. | Zbl | JFM
[21] , Integral representation for the trajectories of control system with generalized right-hand side (in Russian), Differentsialnye Uravnenia, Vol. 24, 1988, pp. 1551-1564. English transl.: Differential Equations, Vol. 24, 1988, pp. 1021-1031. | Zbl | MR
[22] , The index of the second variation of the control system, Matem. Sbornik, Vol. 113, 1980, pp. 464-486. English transl. in: Math. USSR Sbornik, Vol. 41, 1982, pp. 383-401. | Zbl | MR
[23] , A Cornucopia of Abnormal Sub Riemannian Minimizers. Part I: the Four-Dimensional Case, IMA Preprint Series #1073,1992. | MR
[24] and , Shortest Paths for Sub-Riemannian Metrics on Rank-2 Distributions, Preprint, 1993.
[25] , Lectures on the Calculus of Variations and Optimal Control Theory, Chelsea, New York, 1980.
[26] and , Strong Minimality of Abnormal Geodesics for 2-Distributions, J. of Dynamical and Control Systems, Vol. 1, 1995, pp. 139-176. | Zbl | MR






