V. I. Arnold, Supplementary chapters to the theory of ordinary differential equations Translation: Geometric methods in the theory of ordinary differential equations, 1978.

V. I. Arnold, Mathematical methods of classical mechanics, 1979.

D. Bao, S. S. Chern, and Z. Shen, An introduction to Riemann-Finsler geometry, 2000.
DOI : 10.1007/978-1-4612-1268-3

R. Battin, An introduction to the mathematics and methods of astrodynamics, rev, 1999.

J. Betts and S. Erb, Optimal Low Thrust Trajectories to the Moon, SIAM Journal on Applied Dynamical Systems, vol.2, issue.2, pp.144-170, 2003.
DOI : 10.1137/S1111111102409080

N. Bogoliubov and Y. A. Mitropolsky, Les methodes asymptotiques en theorie des oscillators nonlineares, 1962.

A. Bombrun and J. Pomet, The Averaged Control System of Fast-Oscillating Control Systems, SIAM Journal on Control and Optimization, vol.51, issue.3, pp.2280-2305, 2013.
DOI : 10.1137/11085791X

URL : https://hal.archives-ouvertes.fr/hal-00648330

B. Bonnard and J. Caillau, Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.24, issue.3, pp.395-411, 2007.
DOI : 10.1016/j.anihpc.2006.03.013

URL : https://hal.archives-ouvertes.fr/hal-00540258

B. Bonnard and J. Caillau, Geodesic flow of the averaged controlled Kepler equation, Forum Mathematicum, vol.21, issue.5, pp.797-814, 2009.
DOI : 10.1515/FORUM.2009.038

URL : https://hal.archives-ouvertes.fr/hal-00134702

B. Bonnard, J. Caillau, and R. Dujol, Energy minimization of single input orbit transfer by averaging and continuation, Bulletin des Sciences Math??matiques, vol.130, issue.8, pp.707-719, 2006.
DOI : 10.1016/j.bulsci.2006.03.005

URL : https://hal.archives-ouvertes.fr/hal-00540255

B. Bonnard, J. Caillau, R. Sinclaire, 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, J. Caillau, and E. Trélat, Geometric optimal control of elliptic Keplerian orbits, Discrete Cont. Dyn-B, vol.5, issue.4, pp.929-956, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00086345

B. Bonnard, J. Caillau, and G. Picot, Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer Towards Circular Orbits, Acta Applicandae Mathematicae, vol.41, issue.3, pp.47-80, 2014.
DOI : 10.1007/s10440-014-9948-2

URL : https://hal.archives-ouvertes.fr/hal-00918633

B. Bonnard, H. Henninger, and J. Rouot, Lunar Perturbation of the Metric Associated to the Averaged Orbital Transfer, In Springer INdAM Series, vol.11, 2015.
DOI : 10.1007/978-3-319-06917-3_3

URL : https://hal.archives-ouvertes.fr/hal-01090977

B. Bonnard, H. Henninger, J. Pomet, and J. Nem?ova, Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer Towards Circular Orbits, Acta Applicandae Mathematicae, vol.41, issue.3, pp.47-80, 2014.
DOI : 10.1007/s10440-014-9948-2

URL : https://hal.archives-ouvertes.fr/hal-00918633

B. Bonnard and D. Sugny, Optimal Control with Applications in space and quantum dynamics, AIMS

A. E. Bryson, Applied Optimal Control: Optimization, Estimation, and Control, IEEE Transactions on Systems, Man, and Cybernetics, vol.9, issue.6, 1975.
DOI : 10.1109/TSMC.1979.4310229

K. M. Carlson, An analytical solution to patched conic trajectories satisfying initial and final boundary conditions, NASA, 1970.

C. Carathéodory, A Calculus of variations and partial differential equations of the first order. Part I: Partial differential equations of the first order, 1965.

L. M. Celnikier, Basics of space flight, Atlantica Séguier Frontières, 1993.

A. Celletti and L. Chiercha, KAM Stability for a three-body problem of the Solar system, Zeitschrift f??r angewandte Mathematik und Physik, vol.57, issue.1, pp.33-41, 2005.
DOI : 10.1007/s00033-005-0002-0

F. Chaplais, Averaging and Deterministic Optimal Control, SIAM Journal on Control and Optimization, vol.25, issue.3, pp.767-780, 1987.
DOI : 10.1137/0325044

URL : https://hal.archives-ouvertes.fr/hal-00654159

O. Cots, Contrôle optimal géométrique: méthodes homotopiques et applications. PhD. Diss, 2012.

B. Daoud, Contribution au contrôle optimal du problème circulaire restreint des trois corps. PhD. Diss, 2011.

T. Dargent, Initial and final boundaries transformation when solving optimal control problem with averaging techniques and application to low thrust orbital transfer. Presented at 66th International Astronautical Congress, 2015.

R. C. Domingos, R. Vilhena-de-moraes, A. F. Bertachini-de-almeida, and . Prado, Third-Body Perturbation in the Case of Elliptic Orbits for the Disturbing Body, Mathematical Problems in Engineering, vol.23, issue.3, 2008.
DOI : 10.1007/BF01229141

T. N. Edelbaum, Propulsion Requirements for Controllable Satellites, ARS Journal, vol.31, issue.8, 1961.
DOI : 10.2514/8.5723

T. N. Edelbaum, Optimum low-thrust rendezvous and station keeping, AIAA Journal, vol.2, issue.7, pp.1196-1201, 1964.
DOI : 10.2514/3.2521

T. N. Edelbaum, Optimum power-limited orbit transfer in strong gravity fields, AIAA Journal, vol.3, issue.5, pp.921-925, 1965.
DOI : 10.2514/3.3016

A. F. Filippov, Differential equations with discontinuous right-hand side, Mat. Sb, vol.93, issue.1, pp.99-128, 1960.
DOI : 10.1090/trans2/042/13

S. Geffroy, Généralisation des techniques de moyennation en contrôle optimal -Application aux problèmes de rendez-vous orbitaux en poussée faible, 1997.

S. Geffroy and R. Epenoy, Optimal low-thrust transfers with constraints---generalization of averaging techniques, Acta Astronautica, vol.41, issue.3, pp.133-149, 1997.
DOI : 10.1016/S0094-5765(97)00208-7

S. Geffroy, Moyennation des problèmes de contrôle optimal à temps final libre -application aux problèmes de transfert et de rendez-vous à poussée faible en temps minimum, CNES Report, CT/TI, pp.96-101, 1996.

G. Gómez, J. Llibre, R. Martínez, and C. Simó, Dynamics and misson design near libration points. Vol II Fundamentals: the case of triangular libration points, World Scientific, 2001.

J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields, 1993.

T. Haberkorn, Transfert orbital à poussée faible avec minimisation de la consommation : resolution par homotopie différentielle, PhD. Diss. INPT-ENSEEIHT, 2004.

P. Hartman, Ordinary Differential Equations, Birkhäuser, 1982.

M. W. Hirsch, S. Smale, and R. L. Devaney, Differential equations, dynamical systems, and an introduction to chaos, 2012.

H. Jeffreys, The earth. Its origin, history and physical constitution (4th, 1959.

V. Jurdjevic, Geometric Control Theory, 1997.
DOI : 10.1017/CBO9780511530036

J. A. Kechichian, Reformulation of Edelbaum's Low-Thrust Transfer Problem Using Optimal Control Theory, Journal of Guidance, Control, and Dynamics, vol.20, issue.5, pp.988-994, 1997.
DOI : 10.2514/2.4145

Y. Kozai, The earth gravitational potential derived from satellite motion, Space Science Reviews, vol.5, issue.6, pp.818-879, 1966.
DOI : 10.1007/BF00173105

A. Machuy, A. F. , -. Prado, and T. Stuchi, Gravitational capture using a four-body model, WSEAS Trans. Math, vol.10, issue.8, pp.573-582, 2002.

G. Mingotti, F. Topputo, and F. Bernelli-zazzera, Low-energy, low-thrust transfers to the Moon, Celestial Mechanics and Dynamical Astronomy, vol.1065, issue.1-3, pp.1-3, 2009.
DOI : 10.1007/s10569-009-9220-7

V. V. Nemytskii and V. V. Stepanov, Qualitative theory of differential equations, NJ, 1960.
DOI : 10.1515/9781400875955

J. A. O-'keefe, A. Eckels, and R. K. Squires, The gravitational field of the earth, The Astronomical Journal, vol.64, p.245, 1959.
DOI : 10.1086/107928

K. Oshima and T. Yanao, Gravity assist in the Sun-Earth-Moon-spacecraft 4-body system, Astron. J, vol.64, p.245, 1959.

G. Pascoli, Eléments de mécanique céleste, 1993.

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.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes: the art of scientific computing (3rd, 2007.

A. E. Roy, Luni-solar perturbations of an Earth satellite, Astrophysics and Space Science, vol.9, issue.4, pp.375-386, 1969.
DOI : 10.1007/BF00651343

U. Serres, On Zermelo-Like Problems: Gauss???Bonnet Inequality and E. Hopf Theorem, Journal of Dynamical and Control Systems, vol.11, issue.2, pp.99-131, 2009.
DOI : 10.1007/s10883-008-9056-6

URL : https://hal.archives-ouvertes.fr/hal-00705931

U. Serres, On the curvature of two-dimensional optimal control systems and Zermelo???s navigation problem, Journal of Mathematical Sciences, vol.3, issue.4, pp.3224-3243, 2006.
DOI : 10.1007/s10958-006-0153-3

V. Szebehely, Theory of orbits in the restricted problem of three bodies, 1967.

V. Volosov, Some types of computations in the theory of nonlinear oscillators which involve averaging, Zh. Vychisl. Mat i Mat Fiz, vol.3, issue.1, 1963.

J. P. Vinti, G. J. Der, and N. L. Bonativo, Orbital and celestial mechanics, 1998.
DOI : 10.2514/4.866487

O. Zarrouati, Trajectories spatiales, CEPADUES-EDITIONS, 1987.

V. N. Zharkov, Interior structure of the Earth and planets, 1986.