A. Agrachev, G. Stefani, and P. Zezza, Strong optimality for a bang-bang trajectory, SIAM J. Control Optim, vol.41, pp.991-1014, 2002.

A. A. Agrachev and C. Biolo, Switching in time-optimal problem: the 3d case with 2d control, J. Dynamical and Control Systems, pp.1-19, 2016.

A. A. Agrachev and C. Biolo, Optimality of broken extremals, J. Dynamical and Control Systems
DOI : 10.1007/s10883-018-9416-9
URL : http://arxiv.org/pdf/1709.07775

A. A. Agrachev and Y. L. Sachkov, Control theory from the geometric viewpoint, Control Theory and Optimization, vol.87, 2004.
DOI : 10.1007/978-3-662-06404-7

V. I. Arnold, Mathematical methods of classical mechanics, Graduate Texts in Mathematics, vol.60, 1989.

V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, , 1987.

M. Audin, Exemples de hamiltoniens non intégrables en mécanique analytique réelle, vol.12, pp.1-23, 2003.
DOI : 10.5802/afst.1042
URL : http://afst.cedram.org/cedram-bin/article/AFST_2003_6_12_1_1_0.pdf

M. Ayoul and T. Z. Nguyen, Galoisian obstructions to non-hamiltonian integrability, Comptes Rendus Mathematiques, vol.348, 2009.
DOI : 10.1016/j.crma.2010.10.024
URL : https://hal.archives-ouvertes.fr/hal-00629206

D. Barilari, Y. Chitour, F. Jean, D. Prandi, and M. Sigalotti, On the regularity of abnormal minimizers for rank 2 sub-riemannian structures, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01757343

V. V. Beletsky, Essays on the motion of celestial bodies, 2001.
DOI : 10.1115/1.1623753

I. Bendixson, Sur les courbes définies par des équations différentielles, Acta Mathematica, vol.24, issue.1, pp.1-88, 1901.

C. Biolo, Switching in time optimal problems, 2018.

A. Bombrun and J. Pomet, The averaged control system of fast oscillating control systems, SIAM J. on Control Optim, vol.51, pp.2280-2305, 2013.
DOI : 10.1137/11085791x
URL : https://hal.archives-ouvertes.fr/hal-00648330

B. Bonnard, T. Combot, and L. Jassionnesse, Integrability methods in the time minimal coherence transfer for Ising chains of three spins, Discrete Contin. Dyn. Syst. Ser. A, vol.23, pp.609-635, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00969285

B. Bonnard, H. C. Henninger, J. N?mcová, and J. Pomet, Time versus energy in the averaged optimal coplanar kepler transfer towards circular orbits, Acta Applicandae Mathematicae, vol.135, issue.1, pp.47-80, 2015.
DOI : 10.1007/s10440-014-9948-2
URL : https://hal.archives-ouvertes.fr/hal-00918633

J. Bonnard, B. Caillau, and G. Janin, Conjugate and cut loci of a two-sphere of revolution with application to optimal control, Ann. Inst. Henri Poincaré Anal. Non Linéaire, vol.26, pp.1081-1098, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00212075

R. Braddell, A. Delshams, E. Miranda, C. Oms, and A. Planas, An invitation to singular symplectic geometry, 2018.
DOI : 10.1142/s0219887819400085
URL : http://arxiv.org/pdf/1705.03846

J. Caillau and B. Bonnard, Introduction to nonlinear optimal control, Advanced topics in control systems theory, vol.328, pp.1-60, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00540265

J. Caillau, Z. Chen, and Y. Chitour, L 1-minimization for mechanical systems, SIAM J. Control Optim, vol.54, pp.1245-1265, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01136676

J. Caillau and B. Daoud, Minimum time control of the restricted three-body problem, SIAM Journal on Control and Optimization, vol.50, issue.6, pp.3178-3202, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00599216

J. Caillau, B. Daoud, and J. Gergaud, On some Riemannian aspects of the two and three-body controlled problems, Recent Advances in Optimization and its Applications in Engineering, pp.205-224, 2009.

J. Caillau, J. Féjoz, M. Orieux, and R. Roussarie, Singularities of min. time affine control systems, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01718345

J. Caillau and J. Noailles, Coplanar control of a satellite around the earth, ESAIM: COCV, vol.6, pp.239-258, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00540251

L. Cesari, Optimization-Theory and Applications. Problems with Ordinary Differential Equations, 1983.

T. Combot, Non-integrability of the equal mass n-body problem with non-zero angular momentum, Celestial Mech. Dynam. Astronom, vol.114, issue.4, pp.319-340, 2012.

T. Combot and C. Sanabria, A symplectic kovacic's algorithm in dimension 4, Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation, pp.143-150, 2018.
DOI : 10.1145/3208976.3209005
URL : http://dl.acm.org/ft_gateway.cfm?id=3209005&type=pdf

F. Dumortier, Techniques in the theory of local bifurcations: Blow-up, normal forms, nilpotent bifurcations, singular perturbations, 1993.

I. Ekeland, Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations, Publications mathématiques de l'I.H.É.S, vol.47, pp.5-32, 1977.
DOI : 10.1007/bf02684338
URL : http://www.numdam.org/article/PMIHES_1977__47__5_0.pdf

J. Féjoz and L. Kaczmarek, Sur le théorème de Bertrand (d'après Michael Herman), Ergodic Theory Dynam. Systems, vol.24, issue.5, pp.1583-1589, 2004.

J. Féjoz, Introduction to K.A.M. theory, with a view to celestial mechanics. Variational methods in imaging and geometric control, 2016.

M. Gowda, Inverse and implicit function theorems for h-differentiable and semismooth functions, Optimization and Software, vol.19, pp.443-461, 2004.
DOI : 10.1080/10556780410001697668
URL : http://www.math.umbc.edu/~gowda/tech-reports/tr00-08.pdf

H. Hermes, Nilpotent and higher order approximations of vector field systems, SIAM Reviews, vol.33, pp.238-264, 1991.
DOI : 10.1137/1033050

M. Hirsch, C. C. Pugh, and M. Shub, , vol.583, 2006.

E. , Bruns' theorem: the proof and some generalizations, Celestial Mech. Dynam. Astronom, vol.76, issue.4, pp.241-281, 2000.

V. Jurdjevic, Geometric control theory, 2008.

T. Kimura, On riemann's equations which are solvable by quadratures, Funkcial. Ekvac, vol.12, p.1970, 1969.

J. Lournond, De la complexité d'un créneau, Journées Nationales d'Albi, 1996.

B. Malgrange, Ideals of differentiable functions, 1966.

H. Maurer and N. Osmolovskii, Second order sufficient conditions for time optimal bang-bang control, SIAM J. Control Optim, vol.42, pp.239-2263, 2004.

J. J. Morales-ruiz, Differential Galois theory and non-integrability of Hamiltonian systems, 1999.

J. J. Morales-ruiz and J. P. Ramis, Galoisian obstructions to integrability of Hamiltonian systems, Methods Appl. Anal, vol.8, issue.1, pp.97-111, 2001.

J. J. Morales-ruiz, J. Ramis, and C. Simo, Integrability of Hamiltonian systems and differential Galois groups of higher variational equations, Ann. Sci. École Norm. Sup, vol.40, issue.4, pp.845-884, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00635878

M. Morse, A generalization of the sturm separation and comparison theorems innspace, Mathematische Annalen, vol.103, issue.1, pp.52-69, 1930.

J. K. Moser, Regularization of kepler's problem and the averaging method on a manifold, Comm. Pure Appl. Math, vol.23, pp.609-635, 1970.

M. Orieux, J. Caillau, T. Combot, and J. Féjoz, Non-integrability of the minimum-time kepler problem, Journal of Geom. Phys, vol.132, pp.452-459, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01679261

Y. Osipov, The kepler problem and geodesic flows in spaces of constant curvature, Celestial Mech, vol.16, issue.2, pp.191-208, 1977.

Y. Pesin, Lectures on partial hyperbolicity and stable ergodicity, 2004.

L. Poggiolini and M. Spadini, Bang-bang trajectories with a double switching time in the minimum time problem, ENSAIM: COCV, vol.22, pp.688-709, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01024733

H. Poincaré, Les méthodes nouvelles de la mécanique céleste, 1892.

H. Poincaré, Les méthodes nouvelles de la mécanique céleste, vol.III, 1899.

L. S. Pontryagin, The mathematical theory of optimal processes and differential games, Topology, ordinary differential equations, vol.169, pp.254-255, 1985.

. Robert-h-roussarie, Modeles locaux de champs et de formes. Société mathématique de France, 1976.

J. Sauloy, Differential Galois Theory through Riemann-Hilbert Correspondence: An Elementary Introduction, vol.177, 2016.

M. F. Singer, Introduction to the Galois Theory of Linear Differential Equations. Algebraic Theory of Differential Equations, 2009.

F. Takens, Singularities of vector fields, Publ. Math. IHES, vol.43, issue.47, p.100, 1974.

E. Trélat, Asymptotics of accessibility sets along an abnormal trajectory, ENSAIM: COCV, vol.6, pp.387-414, 2001.

A. V. Tsygvintsev, Non-existence of new meromorphic first integrals in the planar three-body problem, Celestial Mech. Dynam. Astronom, vol.86, issue.3, pp.237-247, 2003.

L. Van-den-dries and C. Miller, The elementary theory of restricted analytic fields with exponentiation, Ann. of Math, vol.140, pp.183-205, 1994.

M. Van-der-put and M. F. Singer, Galois Theory of Linear Differential Equations, vol.328, 2003.

S. L. Ziglin, Branching of solutions and nonexistence of first integrals in hamiltonian mechanics. i. Functional Analysis and Its Applications, vol.16, pp.181-189, 1982.