A. [. Arnold, S. Varchenko, and . Gussein-zadé, Singularities of dierentiable maps, II. Monodromy and asymptotics of integrals, 1988.

]. W. Bal000 and . Balser, Formal power series and linear systems of meromorphic ordinary dierential equations. Universitext, 2000.

]. E. Bor28 and . Borel, Leçons sur les séries divergentes. Gauthier-Villars, 1928.

]. B. Bra91 and . Braaksma, Multisummability and Stokes multipliers of linear meromorphic dierential equations, J. Dierential Equations, vol.92, issue.1, pp.45-75, 1991.

C. [. Berry and . Howls, Hyperasymptotics for Integrals with Saddles, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.434, issue.1892, pp.657-675, 1991.
DOI : 10.1098/rspa.1991.0119

C. Candelpergher, F. Nosmas, and . Pham, Approche de la résurgence, Actualités mathématiques, 1993.

]. B. Candelpergher, C. Nosmas, and F. Pham, Premiers pas en calcul ??tranger, Premiers pas en calcul étranger, pp.201-224, 1993.
DOI : 10.5802/aif.1327

]. O. Cost98 and . Costin, On Borel summation and Stokes phenomena for rank-1 nonlinear systems of ordinary dierential equations, Duke Math, J, vol.93, issue.2, p.289344, 1998.

]. O. Cost001 and R. D. Costin, Costin On the formation of singularities of solutions of nonlinear dierential systems in antistokes directions, Invent. Math, vol.145, issue.3, p.425485, 2001.

]. E. Del94 and . Delabaere, Introduction to the écalle theory, in Computer algebra and dierential equations, pp.59-102, 1994.

]. E. Del010 and . Delabaere, Singular integrals and the stationary phase methods. Algebraic approach to dierential equations, World Sci. Publ, pp.136-209, 2010.

H. [. Delabaere, F. Dillinger, and . Pham, Exact semiclassical expansions for one-dimensional quantum oscillators, Journal of Mathematical Physics, vol.38, issue.12, pp.6126-6184, 1997.
DOI : 10.1063/1.532206

F. [. Delabaere and . Pham, Unfolding the Quartic Oscillator, Annals of Physics, vol.261, issue.2, 1997.
DOI : 10.1006/aphy.1997.5737

E. Delabaere and F. Pham, Eigenvalues of complex Hamiltonians with -symmetry. I, Physics Letters A, vol.250, issue.1-3, pp.25-32, 1998.
DOI : 10.1016/S0375-9601(98)00791-9

F. [. Delabaere and . Pham, Resurgent methods in semi-classical asymptotics, Ann. Inst. Henri Poincaré, Sect. A, vol.71, issue.1, pp.1-94, 1999.

C. [. Delabaere and . Howls, Global asymptotics for multiple integrals with boundaries. Duke Math, J, vol.112, issue.2, pp.199-264, 2002.

E. Delabaere and J. M. Rasoamanana, Resurgent deformation of an ordinary dierential equation of order 2, Pacic Journal of Mathematics, vol.223, issue.1, p.3593, 2006.

D. [. Delabaere and . Trinh, Spectral analysis of the complex cubic oscillator, Journal of Physics A: Mathematical and General, vol.33, issue.48, pp.8771-8796, 2000.
DOI : 10.1088/0305-4470/33/48/314

]. R. Din73 and . Dingle, Asymptotic expansions : their derivation and interpretation, 1973.

J. Écalle, Les algèbres de fonctions résurgentes, Publ. Math. D'Orsay, p.5, 1981.

J. Écalle, Les fonctions résurgentes appliquées à l'itération, Publ. Math. D'Orsay, p.6, 1981.

J. Écalle, Cinq applications des fonctions résurgentes, preprint 84T 62, 1984.

]. J. Ec85 and . Écalle, L'équation du pont et la classication analytique des objets locaux, Publ. Math. D'Orsay, p.5, 1985.

]. J. Ec90 and . Écalle, Finitude des cycles limites et accéléro-sommation de l'application de retour . Bifurcations of planar vector elds, Lecture Notes in Maths N o 1455, 1990.

]. J. Ec92 and . Écalle, Singularités non abordables par la géométrie. Annales de l'Institut Fourier, Fascicule 1 et 2, pp.73-164, 1992.

J. Écalle, Six lectures on transseries, Analysable functions and the Constructive proof of Dulac's conjecture, Bifurcations and periodic orbits of vector elds, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci, vol.408, pp.75-184, 1992.

J. Écalle, Fonctions analysables et preuve constructive de la conjecture de Dulac, Actualités mathématiques, 1993.

]. J. Ec94 and . Écalle, Weighted products and parametric resurgence, Analyse algébrique des perturbations singulières I : Méthodes résurgentes, Travaux en cours, p.749, 1994.

J. Écalle, Twisted resurgence monomials and canonical-spherical synthesis of local objects. Analyzable functions and applications

J. Écalle and F. Menous, Well-behaved convolution averages and the nonaccumulation theorem for limit-cycles. The Stokes phenomenon and Hilbert's 16th problem, 71101, World Sci. Publishing, River Edge, 1995.

]. O. For81 and . Forster, Lectures on Riemann Surfaces, Graduate texts in mathematics, 1981.

D. [. Gelfreich and . Sauzin, Sommation de Borel et ??cart des s??paratrices de l'application de H??non, Annales de l???institut Fourier, vol.51, issue.2, pp.513-567, 2001.
DOI : 10.5802/aif.1831

J. Jost, Riemannian geometry and geometric analysis. Universitext, 1995.

G. Jones and D. Singerman, Complex functions, 1987.
DOI : 10.1017/CBO9781139171915

M. Loday-richaud, Stokes phenomenon, multisummability and differential Galois groups, Annales de l???institut Fourier, vol.44, issue.3, pp.849-906, 1994.
DOI : 10.5802/aif.1419

M. Loday-richaud, Solutions formelles des systèmes diérentiels linéaires méromorphes et sommation, Exposition. Math, vol.13, issue.2-3, p.116162, 1995.

M. Loday-richaud, Rank reduction, normal forms and stokes matrices, Expositiones Mathematicae, vol.19, issue.3
DOI : 10.1016/S0723-0869(01)80003-7

M. Loday-richaud and P. Remy, Resurgence, Stokes phenomenon and alien derivatives for level-one linear dierential systems, Mal85] B. Malgrange, Introduction aux travaux de J. Écalle, pp.31-261, 1985.

]. B. Mal91 and . Malgrange, Equations diérentielles à coecients polynomiaux, Progress in Mathematics, vol.96, 1991.

B. Malgrange, Sommation des séries divergentes, Expositiones Mathematicae, vol.13, pp.163-222, 1995.

J. [. Martinet and . Ramis, Théorie de Galois diérentielle et resommation, Computer Algebra and Dierential Equations, 1984.

J. Martinet and J. P. Ramis, Elementary acceleration and multisummability, Ann. Inst. H. Poincaré, Physique théorique, vol.54, pp.331-401, 1991.

]. F. Men97 and . Menous, The well-behaved Catalan and Brownian averages and their applications to real resummation, Proceedings of the Symposium on Planar Vector Fields (Lleida, p.41, 1996.

F. Menous, Les bonnes moyennes uniformisantes et une application ?? la resommation r??elle, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.8, issue.4, p.628, 1999.
DOI : 10.5802/afst.945

]. A. Old97, Olde Daalhuis, Hyperterminants II, J. Comput. Appl. Math, vol.89, pp.87-95, 1997.

]. A. Old98, Olde Daalhuis, Hyperasymptotic solutions of higher order linear dierential equations with a singularity of rank one, Proc. R. Soc. Lond. A, pp.1-29, 1998.

]. F. Olv74 and . Olver, Asymptotics and special functions, 1974.

D. [. Olivé, T. Sauzin, and . Seara, R??surgence dans une ??quation de Hamilton-Jacobi, Proceedings of the International Conference in Honor of Frédéric Pham, pp.1185-1235, 2003.
DOI : 10.5802/aif.1977

]. F. Ph005 and . Pham, Intégrales singulières. Savoirs actuels, EDP Sciences/CNRS Editions, 2005.

. [. Sauzin, R??surgence param??trique et exponentielle petitesse de l'??cart des s??paratrices du pendule rapidement forc??, Annales de l???institut Fourier, vol.45, issue.2, pp.453-511, 1995.
DOI : 10.5802/aif.1462

D. Sauzin, Resurgent functions and splitting problems, RIMS Kokyuroku, issue.31, pp.1493-1541, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00150994

D. Sauzin, Mould expansions for the saddle-node and resurgence monomials, Renormalization and Galois theories, pp.83-163, 2009.
DOI : 10.4171/073-1/3

URL : https://hal.archives-ouvertes.fr/hal-00197145

D. Sauzin, On the Stability under Convolution of Resurgent Functions, Funkcialaj Ekvacioj, vol.56, issue.3
DOI : 10.1619/fesi.56.397

URL : https://hal.archives-ouvertes.fr/hal-00656739

]. Y. Sib90 and . Sibuya, Linear dierential equations in the complex domain: problems of analytic continuation, 1990.

V. [. Sternin, Shatalov Borel-Laplace transform and asymptotic theory. Introduction to resurgent analysis, 1996.

]. G. Sto and . Stokes, On the Discontinuity of arbitrary constants which appear in divergent developments, Transactions of the Cambridge Philosophical Society

]. J. Tou90 and . Tougeron, An introduction to the theory of Gevrey expansions and to the Borel-Laplace transform with some applications, Canada, 1990.

W. Wasow, Asymptotic expansions for ODE. Interscience pub, 1965.

C. Zhang, Conuence et phénomène de Stokes, J. Math. Sci. Univ. Tokyo, vol.3, issue.1, pp.91-107, 1996.

]. C. Zha99 and . Zhang, Développements asymptotiques q-Gevrey et séries Gq-sommables

]. C. Zha006 and . Zhang, Solutions asymptotiques et méromorphes d'équations aux qdiérences, Théories asymptotiques et équations de Painlevé, pp.341-356, 2006.