V. I. Arnold, Instability of dynamical systems with several degrees of freedom, Sov. Math. Doklady, vol.5, pp.581-585, 1964.

P. Bernard, Homoclinic orbits to invariant sets of quasi-integrable exact maps. Ergodic Theory Dynam, Systems, vol.20, issue.6, pp.1583-1601, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01251209

P. Bernard, Connexions dans les syst??mes lagrangiens d??pendant du temps, Annales de l???institut Fourier, vol.52, issue.5, pp.1533-1568, 2002.
DOI : 10.5802/aif.1924

P. Bernard, The action spectrum near positive definite invariant tori, Bulletin de la Société mathématique de France, vol.131, issue.4, pp.603-616, 2003.
DOI : 10.24033/bsmf.2457
URL : https://hal.archives-ouvertes.fr/hal-01251171

P. Bernard and G. Contreras, A generic property of families of Lagrangian systems, Annals of Mathematics, vol.167, issue.3
DOI : 10.4007/annals.2008.167.1099
URL : https://hal.archives-ouvertes.fr/hal-00294671

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

U. Bessi, An approach to Arnold's diffusion through the calculus of variations. Nonlinear Anal, pp.1115-1135, 1996.

S. Bolotin and D. Treschev, Unbounded growth of energy in nonautonomous Hamiltonian systems, Nonlinearity, vol.12, issue.2, pp.365-388, 1999.
DOI : 10.1088/0951-7715/12/2/013

C. Cheng and J. Yan, Existence of Diffusion Orbits in a priori Unstable Hamiltonian Systems, Journal of Differential Geometry, vol.67, issue.3, pp.457-517, 2004.
DOI : 10.4310/jdg/1102091356

C. Cheng and J. Yan, Arnold diffusion in Hamiltonian systems: a priori unstable case, Journal of Differential Geometry, vol.82, issue.2
DOI : 10.4310/jdg/1246888485

G. Contreras and G. P. Paternain, Connecting orbits between static classes for generic Lagrangian systems, Topology, vol.41, issue.4, pp.645-666, 2002.
DOI : 10.1016/S0040-9383(00)00042-2

G. Contreras, J. Delgado, and R. Iturriaga, Lagrangian flows: The dynamics of globally minimizing orbits-II, Boletim da Sociedade Brasileira de Matem???tica, vol.66, issue.2, pp.155-196, 1997.
DOI : 10.1007/BF01233390

A. Delshams, R. De-la-llave, and T. Seara, A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results, Electronic Research Announcements of the American Mathematical Society, vol.09, issue.16, pp.125-134, 2003.
DOI : 10.1090/S1079-6762-03-00121-5

A. Fathi, Book in preparation

A. Fathi, K. Théorème, and . Et-théorie-de-mather, Th??or??me KAM faible et th??orie de Mather sur les syst??mes lagrangiens, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.324, issue.9, pp.1043-1046, 1997.
DOI : 10.1016/S0764-4442(97)87883-4

A. Fathi, Solutions KAM faibles conjugu??es et barri??res de Peierls, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.325, issue.6, pp.649-652, 1997.
DOI : 10.1016/S0764-4442(97)84777-5

A. Fathi, Orbites h??t??roclines et ensemble de Peierls, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.326, issue.10, pp.1213-1216, 1998.
DOI : 10.1016/S0764-4442(98)80230-9

V. Kaloshin, Geometric proofs of Mather's connecting and accelerating theorems, Topics in dynamics and ergodic theory, pp.310-81, 2003.

Y. Katznelson and D. Ornstein, Twist maps and Aubry-Mather sets. Lipa's legacy, Contemp. Math., Amer. Math. Soc, pp.211-343, 1997.
DOI : 10.1090/conm/211/02829

P. Lochak, Arnold diffusion; a compendium of remarks and questions, in Hamiltonian systems with three or more degrees of freedom, pp.168-183, 1999.

J. P. Marco and D. Sauzin, Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems, Publications math??matiques de l'IH??S, vol.96, issue.1, pp.199-275, 2002.
DOI : 10.1007/s10240-003-0011-5

R. Mañé, Lagrangian flows: The dynamics of globally minimizing orbits, Bol. Soc. Bras. Mat, pp.28-141, 1997.

K. F. Siburg, The principle of least action in geometry and dynamics, Lecture Notes in Mathematics, vol.1844, 2004.
DOI : 10.1007/b97327

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

Z. Xia, Arnold diffusion: a variational construction, Proceedings of the International Congress of Mathematicians, pp.867-877, 1998.

Z. Xia, Arnold Diffusion and instabilities in Hamiltonian dynamics