A. Agrachev, Compactness for sub-Riemannian length minimizers and subanalyticity, Rend. Semin. Mat. Torino, vol.56, pp.1-25, 1999.

A. Agrachev, B. Bonnard, M. Chyba, and I. Kupka, Sub-Riemannian sphere in Martinet flat case, ESAIM: Control, Optimisation and Calculus of Variations, vol.2, pp.377-448, 1997.
DOI : 10.1051/cocv:1997114

A. Agrachev, E. Alaoui, and J. P. Gauthier, Sub-Riemannian metrics on IR 3, Canadian Math. Cont. Proc, vol.25, pp.29-76, 1998.

A. Agrachev, E. Alaoui, J. P. Gauthier, and I. Kupka, Generic singularities of sub- Riemannian on IR 3, pp.377-384, 1996.

A. Agrachev and A. Sarychev, On abnormal extremals for Lagrange variational problems, J. Math. Systems, Estimation and Control, vol.8, issue.1, pp.87-118, 1998.

A. Agrachev and A. Sarychev, Strong minimality of abnormal geodesics for 2-distributions, Journal of Dynamical and Control Systems, vol.113, issue.2, pp.139-176, 1995.
DOI : 10.1007/BF02254637

G. A. Bliss, Lectures on the calculus of variations, 1946.

B. Bonnard, Feedback Equivalence for Nonlinear Systems and the Time Optimal Control Problem, SIAM Journal on Control and Optimization, vol.29, issue.6, pp.1300-1321, 1991.
DOI : 10.1137/0329067

B. Bonnard and M. Chyba, M??thodes g??om??triques et analytiques pour ??tudier l'application exponentielle, la sph??re et le front d'onde en g??om??trie sous-riemannienne dans le cas Martinet, ESAIM: Control, Optimisation and Calculus of Variations, vol.4, pp.245-334, 1999.
DOI : 10.1051/cocv:1999111

B. Bonnard and H. Heutte, La propriété de stricte anormalité est générique, 1995.

B. Bonnard and I. Kupka, Théorie des singularités et optimalité des trajectoires singulì eres dans leprobì eme du temps minimal, Forum Math, vol.5, pp.111-159, 1991.
DOI : 10.1515/form.1993.5.111

B. Bonnard and I. Kupka, Generic properties of singular trajectories, Annales de l'IHP, Analyse non linéaire, pp.167-186, 1997.

B. Bonnard, G. Launay, and E. Trélat, The transcendence we need to compute the sphere and wave front in Martinet SR-geometry, Contemporary Mathematics and its Applications English version in Journal of Mathematical Sciences (Kluwer), vol.64, issue.103, pp.82-117, 1999.

A. D. Bruno, Local methods in nonlinear differential equations, 1989.
DOI : 10.1007/978-3-642-61314-2

M. Chaperon, Géométrie différentielle et singularités des systèmes dynamiques, pp.138-139, 1986.

M. Chyba, Le cas Martinet en géométrie sous-Riemannienne, 1997.

H. Davis, Introduction to nonlinear differential and integral equations, 1962.

L. Van-den-dries, A. Macintyre, and D. Marker, The Elementary Theory of Restricted Analytic Fields with Exponentiation, The Annals of Mathematics, vol.140, issue.1, pp.183-205, 1994.
DOI : 10.2307/2118545

L. Van-den-dries and C. Miller, Geometric categories and o-minimal structures, Duke Math, J, vol.84, issue.2, pp.497-540, 1996.

H. Heutte, Propriétés génériques des extrémalessingulì eres dans le cas multientrée, 1995.

A. J. Krener, The High Order Maximal Principle and Its Application to Singular Extremals, SIAM Journal on Control and Optimization, vol.15, issue.2, pp.256-293, 1977.
DOI : 10.1137/0315019

I. Kupka, Abnormal extremals, Preprint, 1992.

I. Kupka, Géométrie sous-Riemannienne, Séminaire Bourbaki, p.96, 1995.

D. F. Lawden, Elliptic functions and applications, 1980.
DOI : 10.1007/978-1-4757-3980-0

E. B. Lee and L. Markus, Foundations of optimal control theory, 1967.

J. M. Lion and J. P. Rolin, Théorèmes de préparation pour les fonctions logarithmico-exponentielles, Annales de l'Institut Fourier, Fasc, vol.47, issue.3, pp.859-884, 1997.
DOI : 10.5802/aif.1583

URL : http://archive.numdam.org/article/AIF_1997__47_3_859_0.pdf

W. S. Liu and H. J. Sussmann, Shortest paths for sub-Riemannian metrics on rank-two distributions, Memoirs of the American Mathematical Society, vol.118, issue.564, 1995.
DOI : 10.1090/memo/0564

S. Lojasiewicz and H. J. Sussmann, Some Examples of Reachable Sets and Optimal Cost Functions That Fail to be Subanalytic, SIAM Journal on Control and Optimization, vol.23, issue.4, pp.584-598, 1985.
DOI : 10.1137/0323037

A. E. Love, A treatise of the mathematica theory of elasticity, 1944.

A. S. Mischenko, Lagrangian manifolds and the Maslov operator, 1980.

R. Montgomery, Abnormal Minimizers, SIAM Journal on Control and Optimization, vol.32, issue.6, pp.1605-1620, 1997.
DOI : 10.1137/S0363012993244945

R. Moussu and A. Roche, Th???orie de Hovanskii et probl???me de Dulac, Inventiones Mathematicae, vol.24, issue.I, pp.431-441, 1991.
DOI : 10.1007/BF01232274

L. Pontriaguine, Théorie mathématique des processus optimaux, 1974.

R. Roussarie, Bifurcations of planar vector fields and Hilbert's 16th problem, Birkhäuser, 1998.

Y. L. Sachkov, Symmetries of flat rank two distributions and sub-Riemannian structures, 1998.

E. Trélat, Some properties of the value function and its level sets for affine control systems with quadratic cost, Journal of Dynamical and Control Systems, vol.6, issue.4, pp.511-541, 2000.
DOI : 10.1023/A:1009552511132

E. Trélat, Etude asymptotique et transcendance de la fonction valeur en contrôle optimal ; catégorie log-exp dans le cas sous-Riemannien de Martinet, 2000.

E. Trélat, Asymptotics of accessibility sets along an abnormal trajectory, ESAIM Control Optim, Calc. Var, vol.6, pp.387-414, 2001.

E. Trélat, Non-subanalyticity of sub-Riemannian Martinet spheres, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.6
DOI : 10.1016/S0764-4442(01)01882-1

I. Zelenko and M. Zhitomirski, Rigid paths of generic 2-distributions on 3-manifolds, Duke Math, Journal, vol.79, issue.2, pp.281-307, 1995.

M. Zhitomirski, Typical singularities of differential 1-forms and pfaffian equations, Trans. of Math. Monographs AMS, vol.113, 1992.