V. I. Arnold, Instability of dynamical systems with several degrees of freedom, Sov. Math. Dokl, vol.6, pp.581-585, 1964.

M. Berti, L. Biasco, and P. Bolle, Drift in phase space: a new variational mechanism with optimal diffusion time, Journal de Math??matiques Pures et Appliqu??es, vol.82, issue.6, pp.613-664, 2003.
DOI : 10.1016/S0021-7824(03)00032-1

M. Berti and P. Bolle, A functional analysis approach to Arnold diffusion Annales de lInstitut Henri Poincare (C) Non Linear Analysis, pp.395-450, 2002.

U. Bessi, L. Chierchia, and E. Valdinoci, Upper bounds on Arnold diffusion times via Mather theory, Journal de Math??matiques Pures et Appliqu??es, vol.80, issue.1, pp.105-129, 2001.
DOI : 10.1016/S0021-7824(00)01188-0

H. W. Broer, H. M. Osinga, and G. Vegter, Algorithms for computing normally hyperbolic invariant manifolds, Zeitschrift f??r angewandte Mathematik und Physik, vol.48, issue.3, pp.480-524, 1997.
DOI : 10.1007/s000330050044

L. Chierchia and G. Gallavotti, Drift and diffusion in phase space, Ann. Inst. H.Poincaré, vol.60, pp.1-144, 1994.

B. V. Chirikov, Research concerning the theory of nonlinear resonance and stochasticity, Institute of Nuclear Physics Engl. Trans., CERN Trans, pp.71-111, 1969.

A. Delshams, R. De-la-llave, and T. M. Seara, A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model, Memoirs of the American Mathematical Society, vol.179, issue.844, 2006.
DOI : 10.1090/memo/0844

C. Efthymiopoulos, G. Contopoulos, and N. Voglis, Cantori, Islands and Asymptotic Curves in the Stickiness Region. Celestial Mechanics and Dynamical Astronomy, pp.221-230, 1999.

C. Froeschlé, E. Lega, and R. Gonczi, Fast Lyapunov indicators. Application to asteroidal motion, Celestial Mechanics and Dynamical Astronomy, vol.67, issue.1, pp.41-62, 1997.
DOI : 10.1023/A:1008276418601

C. Froeschlé, M. Guzzo, and E. Lega, Graphical Evolution of the Arnold Web: From Order to Chaos, Science, vol.289, issue.5487, p.5487, 2000.
DOI : 10.1126/science.289.5487.2108

C. Froeschlé and E. Lega, On the Structure of Symplectic Mappings. The Fast Lyapunov Indicator: a Very Sensitive Tool, Celestial Mechanics and Dynamical Astronomy, pp.167-195, 2000.

C. Froeschlé, M. Guzzo, and E. Lega, Local and global diffusion along resonant lines in discrete quasi?integrable dynamical systems, Celestial Mechanics and Dynamical Astronomy, vol.92, pp.1-3, 2005.

M. Guzzo, E. Lega, and C. Froeschlé, On the numerical detection of the effective stability of chaotic motions in quasi-integrable systems, Physica D: Nonlinear Phenomena, vol.163, issue.1-2, 2002.
DOI : 10.1016/S0167-2789(01)00383-9

M. Guzzo, E. Lega, and C. Froeschlé, First Numerical Evidence of Arnold diffusion in quasi?integrable systems, DCDS B, vol.5, issue.3, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00388279

M. Guzzo, E. Lega, and C. Froeschlé, Diffusion and stability in perturbed non-convex integrable systems, Nonlinearity, vol.19, issue.5, pp.1049-1067, 2006.
DOI : 10.1088/0951-7715/19/5/003

URL : https://hal.archives-ouvertes.fr/hal-00388613

M. Hénon and C. Heiles, The applicability of the third integral of motion: Some numerical experiments, The Astronomical Journal, vol.69, pp.73-79, 1964.
DOI : 10.1086/109234

B. Hasselblatt and Y. Pesin, Partially hyperbolic dynamical systems. Handbook of dynamical systems, pp.1-55, 2006.
DOI : 10.1016/s1874-575x(06)80026-3

B. Krauskopf, H. M. Osinga, E. J. Doedel, . Henderson, J. Enheimer et al., A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS, International Journal of Bifurcation and Chaos, vol.15, issue.03, pp.763-791, 2005.
DOI : 10.1142/S0218127405012533

T. Konishi and K. Kaneko, Diffusion in Hamiltonian chaos and its size dependence, Journal of Physics A: Mathematical and General, vol.23, issue.15, pp.715-720
DOI : 10.1088/0305-4470/23/15/004

J. Laskar, Frequency analysis for multi-dimensional systems. Global dynamics and diffusion, Physica D: Nonlinear Phenomena, vol.67, issue.1-3, pp.257-281, 1993.
DOI : 10.1016/0167-2789(93)90210-R

E. Lega, M. Guzzo, and C. Froeschlé, Detection of Arnold diffusion in Hamiltonian systems, Physica D: Nonlinear Phenomena, vol.182, issue.3-4, pp.179-187, 2003.
DOI : 10.1016/S0167-2789(03)00121-0

E. Lega, C. Froeschlé, and M. Guzzo, Diffusion in Hamiltonian quasi?integrable systems Topics in gravitational dynamics, In Lecture Notes in Physics, vol.729, 2007.

A. Lichtemberg and M. A. Aswani, Arnold diffusion in many weakly coupled mappings, Physical Review E, vol.57, issue.5, pp.5325-5321, 1998.
DOI : 10.1103/PhysRevE.57.5325

R. S. Mackay, J. D. Meiss, and I. C. Percival, Transport in Hamiltonian systems, Physica D: Nonlinear Phenomena, vol.13, issue.1-2, pp.55-81, 1984.
DOI : 10.1016/0167-2789(84)90270-7

E. Manoukian, Modern Concepts and Theorems of Mathematical Statistics, 1986.
DOI : 10.1007/978-1-4612-4856-9

C. Simo, On the analytical and numerical approximation of invariant manifolds, in Modern Methods in Celestial Mechanics, Benest, Cl. Froeschlé eds, EditionsFrontì eres, pp.285-329, 1989.

C. Simo and C. Valls, A formal approximation of the splitting of separatrices in the classical Arnold's example of diffusion with two equal parameters, Nonlinearity, vol.14, issue.6, pp.1707-1760, 2001.
DOI : 10.1088/0951-7715/14/6/316

D. Treschev, unstable Hamiltonian systems, Nonlinearity, vol.15, issue.6, pp.2033-2052, 2002.
DOI : 10.1088/0951-7715/15/6/313

D. Treschev, unstable Hamiltonian systems, Nonlinearity, vol.17, issue.5, pp.1803-1841, 2004.
DOI : 10.1088/0951-7715/17/5/014

H. Varvoglis, Chaos, random walks and diffusion in Hamiltonian systems, Hamiltonian systems and Fourier Analysis, pp.247-287, 2005.

B. P. Wood, A. Lichtenberg, and M. A. Lieberman, Arnold diffusion in weakly coupled standard maps, Physical Review A, vol.42, issue.10, pp.5885-5893, 1990.
DOI : 10.1103/PhysRevA.42.5885