A. Agrachev, U. Boscain, and M. Sigalotti, A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds, Discrete Contin. Dyn. Syst, vol.20, issue.4, pp.801-822, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00097173

V. I. Arnold, Mathematical Methods of Classical Mechanics. Translated from the Russian by K. Vogtmann and A. Weinstein, 1989.

M. Audin, Les systèmes hamiltoniens et leur intégrabilité, French) [Hamiltonian Systems and Their Integrability] Cours Spécialisés [Specialized Courses], 8. Société Mathématique de France, 2001.

D. Birkhoff, Dynamical Systems, American society colloquium publications, 1927.

A. V. Bolsinov and A. T. Fomenko, Integrable Geodesic Flows on Two-Dimensional Surfaces, Monographs in contemporary mathematrics, 2000.

B. Bonnard, J. Caillau, R. Sinclair, and M. Tanaka, Conjugate and cut loci of a two-sphere of revolution with application to optimal control, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.4, pp.1081-1098, 2009.
DOI : 10.1016/j.anihpc.2008.03.010

URL : https://hal.archives-ouvertes.fr/hal-00212075

B. Bonnard, O. Cots, and L. Jassionnesse, Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces, to appear in INDAM Volume on meeting on Geometric Control and sub-Riemannian Geometry, 2012.

B. Bonnard, O. Cots, J. Pomet, and N. Shcherbakova, Riemannian metrics on 2D-manifolds related to the Euler???Poinsot rigid body motion, ESAIM: Control, Optimisation and Calculus of Variations, vol.20, issue.3, 2014.
DOI : 10.1051/cocv/2013087

URL : https://hal.archives-ouvertes.fr/hal-00918587

U. Boscain, T. Chambrion, and G. Charlot, Nonisotropic 3-level quantum systems: complete solutions for minimum time and minimum energy, Discrete Contin, Dyn. Syst. Ser. B, vol.5, issue.4, pp.957-990, 2005.

J. Itoh and K. Kiyohara, The cut loci and the conjugate loci on ellipsoids, manuscripta mathematica, vol.114, issue.2, pp.247-264, 2004.
DOI : 10.1007/s00229-004-0455-z

J. Itoh and K. Kiyohara, Cut loci and conjugate loci on Liouville surfaces, Manuscripta Mathematica, vol.96, issue.1-2, pp.115-141, 2011.
DOI : 10.1007/s00229-011-0433-1

V. Jurdjevic, Geometric Control Theory, Studies in Advanced Mathematics, 52, 1997.

N. Khaneja, S. J. Glaser, and R. Brockett, Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer, Physical Review A, vol.65, issue.3, p.65, 2002.
DOI : 10.1103/PhysRevA.65.032301

J. J. Kovacic, An algorithm for solving second order linear homogeneous differential equations, Journal of Symbolic Computation, vol.2, issue.1, pp.3-43, 1986.
DOI : 10.1016/S0747-7171(86)80010-4

D. F. Lawden, Elliptic Functions and Applications, Applied Mathematical Sciences, vol.80, 1989.
DOI : 10.1007/978-1-4757-3980-0

H. Levitt, Spin Dynamics ? Basics of Nuclear Magnetic Resonance, 2001.

J. J. Morales-ruiz and J. Ramis, Integrability of Dynamical Systems Through Differential Galois Theory: A Practical Guide. Differential algebra, complex analysis and orthogonal polynomials 143220, Contemp. Math, vol.509
URL : https://hal.archives-ouvertes.fr/hal-00629721

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes. Translated from the Russian by K. N. Trirogoff, 1962.

M. Singer and F. Ulmer, Galois Groups of Second and Third Order Linear Differential Equations, Journal of Symbolic Computation, vol.16, issue.1, pp.9-36, 1993.
DOI : 10.1006/jsco.1993.1032

M. Van-der-put and M. Singer, Galois Theory of Linear Differential Equations, 2003.
DOI : 10.1007/978-3-642-55750-7

H. Yuan, R. Zeier, and N. Khaneja, Elliptic functions and efficient control of Ising spin chains with unequal couplings, Physical Review A, vol.77, issue.3, p.32340, 2008.
DOI : 10.1103/PhysRevA.77.032340