M. Arnaud, Three results on the regularity of the curves that are invariant by an exact symplectic twist map, Publications math??matiques de l'IH??S, vol.130, issue.8, pp.1-17, 2009.
DOI : 10.1007/s10240-009-0017-8

M. Arnaud, A nondifferentiable essential irrational invariant curve for a $C^1$ symplectic twist map, Journal of Modern Dynamics, vol.5, issue.3, pp.583-591, 2011.
DOI : 10.3934/jmd.2011.5.583
URL : https://hal.archives-ouvertes.fr/hal-00588781

M. Arnaud, The link between the shape of the irrational Aubry-Mather sets and their Lyapunov exponents, Annals of Mathematics, vol.174, issue.3, pp.174-177, 2011.
DOI : 10.4007/annals.2011.174.3.4

M. Arnaud, Boundaries of instability zones for symplectic twist??maps, Journal of the Institute of Mathematics of Jussieu, vol.98, issue.122, pp.13-14, 2013.
DOI : 10.1007/BF01209326
URL : https://hal.archives-ouvertes.fr/hal-00691483

M. Arnaud, Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting, Ergodic Theory and Dynamical Systems, pp.693-712, 2013.

M. Arnaud and &. P. Berger, The non-hyperbolicity of irrational invariant curves for twist maps and all that follows, Revista Matem??tica Iberoamericana, vol.32, issue.4, p.1087349
DOI : 10.4171/RMI/917
URL : https://hal.archives-ouvertes.fr/hal-01087349

M. Arnaud, C. Bonatti, and &. S. Crovisier, Dynamiques symplectiques génériques, Ergodic Theory Dynam, Systems, vol.25, issue.5, pp.1401-1436, 2005.

V. Arnol-'d, Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian, Russian) Uspehi Mat, pp.13-40, 1963.

S. Aubry and &. P. Le-daeron, The discrete Frenkel-Kontorova model and its extensions. I. Exact results for the ground-states, Phys, pp.381-422, 1983.

V. Bangert, Mather Sets for Twist Maps and Geodesics on Tori, Dynamics reported Dynam. Report. Ser. Dynam. Systems Appl, vol.1, issue.1, pp.1-56, 1988.
DOI : 10.1007/978-3-322-96656-8_1

G. D. Birkhoff, Surface transformations and their dynamical applications, Acta Mathematica, vol.43, issue.0, pp.1-119, 1920.
DOI : 10.1007/BF02401754

G. D. Birkhoff, Sur l'existence de régions d'instabilité en Dynamique, Ann. Inst. H. Poincaré, vol.2, issue.4, pp.369-386, 1932.

A. Chenciner and L. Dynamique-au-voisinage-d-'un-point-fixe-elliptique-conservatif, The dynamics at the neighborhood of a conservative elliptic fixed point: from Poincaré and Birkhoff to Aubry and Mather, Seminar Bourbaki, vol.84, pp.121-122, 1983.

A. Furman, On the multiplicative ergodic theorem for uniquely ergodic systems, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.33, issue.6, pp.797-815, 1997.
DOI : 10.1016/S0246-0203(97)80113-6

C. Golé, Symplectic twist maps, Global variational techniques Advanced Series in Nonlinear Dynamics, 2001.

D. L. Goroff, Hyperbolic sets for twist maps, Ergodic Theory Dynam, Systems, vol.5, issue.3, pp.337-339, 1985.

S. Hayashi, Connecting Invariant Manifolds and the Solution of the C 1 Stability and ??-Stability Conjectures for Flows, The Annals of Mathematics, vol.145, issue.1, pp.81-137, 1997.
DOI : 10.2307/2951824

M. Herman, Sur la Conjugaison Diff??rentiable des Diff??omorphismes du Cercle a des Rotations, Publications math??matiques de l'IH??S, vol.28, issue.4, pp.5-233, 1979.
DOI : 10.1007/BF02684798

M. Herman, Sur les courbes invariantes par les difféomorphismes de l'anneau, pp.103-104, 1983.

A. Katok, Some remarks on Birkhoff and Mather twist map theorems, Ergodic Theory Dynamical Systems, p.185194, 1982.
DOI : 10.1070/RM1977v032n04ABEH001639

A. Katok and &. B. Hasselblatt, Introduction to the modern theory of dynamical systems. With a supplementary chapter, Encyclopedia of Mathematics and its Applications, 1995.

A. N. Kolmogorov, On conservation of conditionally periodic motions for a small change in Hamilton's function, Russian) Dokl. Akad. Nauk SSSR (N.S.), vol.98, pp.527-530, 1954.

P. and L. Calvez, Propri??t??s dynamiques des r??gions d'instabilit??, Annales scientifiques de l'??cole normale sup??rieure, vol.20, issue.3, pp.443-464, 1987.
DOI : 10.24033/asens.1539

P. and L. Calvez, Aubry-Mather d'un difféomorphisme conservatif de l'anneau déviant la verticale sont en général hyperboliques, (French) [The Aubry-Mather sets of a conservative diffeomorphism of the annulus twisting the vertical are hyperbolic in general, C. R. Acad. Sci. Paris Sér. I Math, vol.306, issue.1, pp.51-54, 1988.

R. Mañé, Quasi-Anosov Diffeomorphisms and Hyperbolic Manifolds, Transactions of the American Mathematical Society, vol.229, pp.351-370, 1977.
DOI : 10.2307/1998515

J. N. Mather, Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology, vol.21, issue.4, pp.457-467, 1982.
DOI : 10.1016/0040-9383(82)90023-4

J. N. Mather, Variational construction of orbits of twist diffeomorphisms, Journal of the American Mathematical Society, vol.4, issue.2, pp.207-263, 1991.
DOI : 10.1090/S0894-0347-1991-1080112-5

H. Rüssman, On the existence of invariant curves of twist mappings of an annulus, Geometric dynamics, Lecture Notes in Math, pp.677-718, 1007.

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