M. Avellaneda, T. Y. Hou, and G. Papanicolaou, Finite difference approximations for partial differential equations with rapidly oscillating coefficients, ESAIM: Mathematical Modelling and Numerical Analysis, vol.25, issue.6, pp.693-710, 1991.
DOI : 10.1051/m2an/1991250606931

W. Bao, Ground states and dynamics of multi-component Bose-Einstein condensates, Multiscale Modeling and Simulation: a, SIAM Interdisciplinary Journal, vol.2, pp.210-236, 2004.

Y. Bugeaud, Approximation by algebraic numbers, Cambridge Tracts in Mathematics, vol.160, 2004.
DOI : 10.1017/CBO9780511542886

URL : https://hal.archives-ouvertes.fr/hal-00093387

M. P. Calvo, P. Chartier, A. Murua, and J. M. Sanz-serna, A Stroboscopic Numerical Method for Highly Oscillatory Problems, Numerical Analysis and Multiscale Computations, pp.73-87, 2011.
DOI : 10.1007/978-3-642-21943-6_4

URL : https://hal.archives-ouvertes.fr/hal-00777182

P. Chartier, N. Crouseilles, M. Lemou, and F. Méhats, Uniformly accurate numerical schemes for highly oscillatory Klein???Gordon and nonlinear Schr??dinger equations, Numerische Mathematik, vol.150, issue.5???7, pp.211-250, 2015.
DOI : 10.1007/s00211-014-0638-9

P. Chartier, J. Makazaga, A. Murua, and G. Vilmart, Multi-revolution composition methods for highly oscillatory differential equations, Numerische Mathematik, vol.6, issue.2, pp.167-192, 2014.
DOI : 10.1007/s00211-013-0602-0

URL : https://hal.archives-ouvertes.fr/hal-00796581

M. P. Calvo, P. Chartier, A. Murua, and J. Sanz-serna, Numerical stroboscopic averaging for ODEs and DAEs, Numerical stroboscopic averaging for ODEs and DAEs, pp.1077-1095, 2011.
DOI : 10.1016/j.apnum.2011.06.007

URL : https://hal.archives-ouvertes.fr/hal-00777181

P. Chartier, A. Murua, and J. M. Sanz-serna, A formal series approach to averaging: Exponentially small error estimates, Discrete and Continuous Dynamical Systems (DCDS-A), 2012.
DOI : 10.3934/dcds.2012.32.3009

URL : https://hal.archives-ouvertes.fr/hal-00777178

P. Chartier, A. Murua, and J. M. Sanz-serna, Higher-Order Averaging, Formal Series and Numerical Integration I: B-series, Foundations of Computational Mathematics, vol.29, issue.6, 2010.
DOI : 10.1007/s10208-010-9074-0

URL : https://hal.archives-ouvertes.fr/inria-00598357

P. Chartier, A. Murua, and J. M. Sanz-serna, Erratum to: Higher-Order Averaging, Formal Series and Numerical Integration II: The Quasi-Periodic Case, Foundations of Computational Mathematics, vol.17, issue.2, 2012.
DOI : 10.1007/s10208-016-9311-2

P. Chartier, A. Murua, and J. M. Sanz-serna, Higher-Order Averaging, Formal Series and Numerical Integration III: Error Bounds, Foundations of Computational Mathematics, vol.17, issue.2, 2013.
DOI : 10.1007/s10208-013-9175-7

URL : https://hal.archives-ouvertes.fr/hal-00922682

E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration. Structure- Preserving Algorithms for Ordinary Differential Equations, Series in Computational Mathematics 31, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01403326

D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates, Physical Review Letters, vol.81, issue.8, pp.1539-1542, 1998.
DOI : 10.1103/PhysRevLett.81.1539

R. Dáger and E. Zuazua, Controllability of star-shaped networks of strings, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.332, issue.7, pp.621-626, 2001.
DOI : 10.1016/S0764-4442(01)01876-6

G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Bulletin of the American Mathematical Society, vol.35, issue.6, 2008.
DOI : 10.1090/S0002-9904-1929-04793-1

B. Grébert and C. Villegas-blas, On the energy exchange between resonant modes in nonlinear Schrödinger equations, Ann. I. H. Poincaré, vol.28, 2011.

J. C. Lagarias, Best simultaneous Diophantine approximations. I. Growth rates of best approximation denominators, Transactions of the American Mathematical Society, vol.272, issue.2, 1982.
DOI : 10.1090/S0002-9947-1982-0662052-7

J. C. Lagarias, Best simultaneous Diophantine approximations. II. Behavior of consecutive best approximations, Pacific Journal of Mathematics, vol.102, issue.1, 1982.
DOI : 10.2140/pjm.1982.102.61

R. Orive and E. Zuazua, Finite Difference Approximation of Homogenization Problems for Elliptic Equations, Multiscale Modeling & Simulation, vol.4, issue.1, pp.36-87, 2005.
DOI : 10.1137/040606314

J. A. Sanders, J. Verhulst, and J. Murdock, Averaging methods in nonlinear dynamical systems, Applied Mathematical Sciences, vol.59, 2007.
DOI : 10.1007/978-1-4757-4575-7

C. Simo, Averaging under fast quasi-periodic forcing, in Hamiltonian Mechanics, Integrability and Chaotic Behavior, NATO Asi Series, vol.331