]. V. Arn61, Arnol'd, Small denominators. I. Mapping the circle onto itself, Izv. Akad. Nauk SSSR Ser. Mat, vol.25, pp.21-86, 1961.

W. Banaszczyk, Inequalities for convex bodies and polar reciprocal lattices inR n II: Application ofK-convexity, Discrete & Computational Geometry, vol.159, issue.3, pp.305-311, 1996.
DOI : 10.1007/BF02711514

M. [. Bugeaud and . Laurent, On exponents of homogeneous and inhomogeneous Diophantine approximation, Moscow Math, J, vol.5, issue.4, pp.747-766, 2005.

L. [. Bounemoura and . Niederman, Th??orie de Nekhoroshev g??n??rique sans petits diviseurs, Annales de l???institut Fourier, vol.62, issue.1, 2011.
DOI : 10.5802/aif.2706

A. Bounemoura, Optimal Stability and Instability for Near-Linear Hamiltonians, Annales Henri Poincar??, vol.3, issue.3, pp.857-868, 2012.
DOI : 10.1007/s00023-011-0137-9

URL : https://hal.archives-ouvertes.fr/hal-00593882

J. W. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Math. and Math. Phys, issue.45, 1957.

W. Davenport and W. M. Schmidt, Approximation to real numbers by quadratic irrationals, Acta Arith, vol.13, issue.99, pp.169-176, 1959.

F. Fassò, Lie series method for vector fields and Hamiltonian perturbation theory, ZAMP Zeitschrift f???r angewandte Mathematik und Physik, vol.29, issue.6, pp.41-843, 1990.
DOI : 10.1007/BF00945838

P. M. Gruber and C. G. Lekkerkerker, Geometry of numbers, 1987.

E. [. Hardy and . Wright, An introduction to the theory of numbers, Bulletin of the American Mathematical Society, vol.35, issue.6, 1954.
DOI : 10.1090/S0002-9904-1929-04793-1

K. Khanin, J. L. Dias, and J. Marklof, Renormalization of multidimensional Hamiltonian flows, Nonlinearity, vol.19, issue.12, pp.2727-2753, 2006.
DOI : 10.1088/0951-7715/19/12/001

]. A. Kol53 and . Kolmogorov, On dynamical systems with an integral invariant on the torus, Doklady Akad, Nauk SSSR (N.S.), vol.93, pp.763-766, 1953.

]. A. Kol54 and . Kolmogorov, On the preservation of conditionally periodic motions for a small change in Hamilton's function, Dokl. Akad. Nauk. SSSR, vol.98, pp.527-530, 1954.

]. C. Lek69 and . Lekkerkerker, Geometry of numbers, 1969.

P. Lochak, Canonical perturbation theory via simultaneous approximation, Russian Mathematical Surveys, vol.47, issue.6, pp.57-133, 1992.
DOI : 10.1070/RM1992v047n06ABEH000965

J. Moser, A rapidly convergent iteration method and non-linear differential equations . II, Ann. Scuola Norm, Sup. Pisa, vol.20, issue.3, pp.499-535, 1966.

L. Niederman, Prevalence of exponential stability among nearly integrable Hamiltonian systems, Ergodic Theory and Dynamical Systems, vol.27, issue.03, pp.905-928, 2007.
DOI : 10.1017/S0143385706000927

H. Rüssmann, Invariant tori in non-degenerate nearly integrable Hamiltonian systems, Regular and Chaotic Dynamics, vol.6, issue.2, pp.119-204, 2001.
DOI : 10.1070/RD2001v006n02ABEH000169

M. Waldschmidt, Topologie des points rationnels, Cours deTroisì eme Cycle, Preprint Univ. P. et M. Curie, vol.95, 1994.

J. Yoccoz, Analytic linearization of circle diffeomorphisms, Lecture Notes in Math, vol.1784, pp.125-173, 1998.
DOI : 10.1007/978-3-540-47928-4_3