H. Arbell and J. Fineberg, Pattern formation in two-frequency forced parametric waves, Physical Review E, vol.65, issue.3, p.36224, 2002.
DOI : 10.1103/PhysRevE.65.036224

W. Balser, From Divergent Power Series to Analytic Functions: Theory and Application of Multisummable Power Series, Lecture Notes in Mathematics, vol.1582, 1994.
DOI : 10.1007/BFb0073564

D. Binks and W. Van-de-water, Nonlinear Pattern Formation of Faraday Waves, Physical Review Letters, vol.78, issue.21, pp.4043-4046, 1997.
DOI : 10.1103/PhysRevLett.78.4043

D. Binks, M. T. Westra, and W. Van-de-water, Effect of Depth on the Pattern Formation of Faraday Waves, Physical Review Letters, vol.79, issue.25, pp.5010-5013, 1997.
DOI : 10.1103/PhysRevLett.79.5010

E. Borel, Leçons sur les Séries Divergentes, 1901.

B. Candelpergher, From Analytic Functions to Divergent Power Series, Harmonic Analysis and Rational Approximation: Their Rôles in Signals, Control and Dynamical Systems, pp.15-37, 2006.
DOI : 10.1007/11601609_2

J. Carr, Applications of Centre Manifold Theory, 1981.
DOI : 10.1007/978-1-4612-5929-9

P. Chossat and G. Iooss, The Couette?Taylor Problem, Applied Mathematical Sciences, vol.102, 1994.
DOI : 10.1007/978-1-4612-4300-7

B. Christiansen, P. Alstrom, and M. T. Levinsen, Ordered capillary-wave states: Quasicrystals, hexagons, and radial waves, Physical Review Letters, vol.68, issue.14, pp.2157-2160, 1992.
DOI : 10.1103/PhysRevLett.68.2157

H. Cohen, A Course in Computational Algebraic Number Theory. Graduate texts in mathematics, 1993.

W. Craig and C. E. Wayne, Newton's method and periodic solutions of nonlinear wave equations, Communications on Pure and Applied Mathematics, vol.20, issue.11, pp.1409-1498, 1993.
DOI : 10.1002/cpa.3160461102

R. De-la-llave, A tutorial on KAM theory, Smooth Ergodic Theory and Its Applications of Proceedings of Symposia in Pure Mathematics, pp.175-292, 2001.
DOI : 10.1090/pspum/069/1858536

W. S. Edwards and S. Fauve, Patterns and quasi-patterns in the Faraday experiment, Journal of Fluid Mechanics, vol.248, issue.-1, pp.123-148, 1994.
DOI : 10.1103/PhysRevLett.54.1524

M. Gevrey, Sur la nature analytique des solutions des ??quations aux d??riv??es partielles. Premier m??moire, Annales scientifiques de l'??cole normale sup??rieure, vol.35, pp.129-190, 1918.
DOI : 10.24033/asens.706

M. Golubitsky, I. Stewart, and D. G. Schaeffer, Singularities and Groups in Bifurcation Theory. Volume II, 1988.

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 1983.

G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Bulletin of the American Mathematical Society, vol.35, issue.6, 1960.
DOI : 10.1090/S0002-9904-1929-04793-1

R. Herrero, E. G. Westhoff, A. Aumann, T. Ackemann, Y. A. Logvin et al., Twelvefold Quasiperiodic Patterns in a Nonlinear Optical System with Continuous Rotational Symmetry, Physical Review Letters, vol.82, issue.23, pp.4627-4630, 1999.
DOI : 10.1103/PhysRevLett.82.4627

G. Iooss and M. Adelmeyer, Topics in Bifurcation Theory and Applications, volume 3 of Advanced Series in Nonlinear Dynamics, 1998.

G. Iooss and P. Plotnikov, Small divisor problem in the theory of threedimensional water gravity waves. Memoirs of the, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01265182

G. Iooss, P. I. Plotnikov, and J. F. Toland, Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity, Archive for Rational Mechanics and Analysis, vol.2, issue.3, pp.367-478, 2005.
DOI : 10.1007/s00205-005-0381-6
URL : https://hal.archives-ouvertes.fr/hal-00009222

C. Janot, Quasicrystals: a Primer, 1994.

A. Kudrolli, B. Pier, and J. P. Gollub, Superlattice patterns in surface waves, Physica D: Nonlinear Phenomena, vol.123, issue.1-4, pp.99-111, 1998.
DOI : 10.1016/S0167-2789(98)00115-8
URL : https://hal.archives-ouvertes.fr/hal-00120028

R. Lifshitz and H. Diamant, Soft quasicrystals???Why are they stable?, Philosophical Magazine, vol.342, issue.18-21, pp.18-213021, 2007.
DOI : 10.1038/nature04722
URL : http://arxiv.org/abs/cond-mat/0611115

J. P. Marco and D. Sauzin, Stability and instability for Gevrey quasiconvex near-integrable Hamiltonian systems, Publications Mathématiques de L'IHÉSIH´IHÉS, pp.199-275, 2003.

J. P. Ramis and R. Schäfke, Gevrey separation of fast and slow variables, Nonlinearity, vol.9, issue.2, pp.353-384, 1996.
DOI : 10.1088/0951-7715/9/2/004

J. L. Rogers, W. Pesch, O. Brausch, and M. F. Schatz, Complex-ordered patterns in shaken convection, Physical Review E, vol.71, issue.6, p.71066214, 2005.
DOI : 10.1103/PhysRevE.71.066214

A. M. Rucklidge and W. J. Rucklidge, Convergence properties of the 8, 10 and 12 mode representations of quasipatterns, Physica D: Nonlinear Phenomena, vol.178, issue.1-2, pp.62-82, 2003.
DOI : 10.1016/S0167-2789(02)00792-3

A. M. Rucklidge and M. Silber, Design of Parametrically Forced Patterns and Quasipatterns, SIAM Journal on Applied Dynamical Systems, vol.8, issue.1, 2009.
DOI : 10.1137/080719066

A. Vanderbauwhede and G. Iooss, Center Manifold Theory in Infinite Dimensions, Dynamics Reported: Expositions in Dynamical Systems (New Series), pp.125-163, 1992.
DOI : 10.1007/978-3-642-61243-5_4

U. E. Volmar and H. W. Muller, Quasiperiodic patterns in Rayleigh-B??nard convection under gravity modulation, Physical Review E, vol.56, issue.5, pp.5423-5430, 1997.
DOI : 10.1103/PhysRevE.56.5423