D. G. Babbitt and V. S. Varadarajan, Local moduli for meromorphic differential equations, Bulletin of the American Mathematical Society, vol.12, issue.1, pp.169-170217, 1989.
DOI : 10.1090/S0273-0979-1985-15300-5

W. Balser, W. B. Jurkat, and D. A. Lutz, A general theory of invariants for meromorphic differential equations. I. Formal invariants, Funkcial. Ekvac, vol.22, issue.2, pp.197-221, 1979.

W. Balser, W. B. Jurkat, and D. A. Lutz, Transfer of connection problems for first level solutions of meromorphic differential equations, and associated Laplace transforms, J. Reine Angew. Math, vol.344, pp.149-170, 1983.

W. Balser, From divergent power series to analytic functions Theory and application of multisummable power series, Lecture Notes in Mathematics, vol.1582, 1994.

W. Balser, Formal power series and linear systems of meromorphic ordinary differential equations, 2000.

B. L. Braaksma, Multisummability and Stokes multipliers of linear meromorphic differential equations, Journal of Differential Equations, vol.92, issue.1, pp.45-75, 1991.
DOI : 10.1016/0022-0396(91)90063-F

B. L. Braaksma, G. K. Immink, and Y. Sibuya, The Stokes phenomenon in exact asymptotics, Pacific Journal of Mathematics, vol.187, issue.1, pp.13-50, 1999.
DOI : 10.2140/pjm.1999.187.13

R. Loday-richaud, Resurgence for level-one linear diff, p.56

P. Deligne, B. Malgrange, and J. Ramis, Singularités irrégulì eres, Documents Mathématiques (Paris) [Mathematical Documents, 2007.

A. Duval and C. Mitschi, Matrices de Stokes et groupe de Galois des ??quations hyperg??om??triques confluentes g??n??ralis??es, Pacific Journal of Mathematics, vol.138, issue.1, pp.25-56, 1989.
DOI : 10.2140/pjm.1989.138.25

. Jeanécallejean´jeanécalle, Les algèbres de fonctions résurgentes, Pub. Math. Orsay, vol.1, pp.81-051, 1981.

. Jeanécallejean´jeanécalle, Les fonctions résurgentes, l'´ equation du pont et la classification des objets locaux, Pub. Math. Orsay, vol.3, pp.85-051, 1985.

. Jeanécallejean´jeanécalle, Singularités non abordables par la géométrie, Ann. Inst. Fourier (Grenoble), vol.42, issue.12, pp.73-164, 1992.

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 différentiels linéaires méromorphes et sommation, Exposition. Math, vol.13, issue.2-3, pp.116-162, 1995.

M. Loday-richaud, Rank reduction, normal forms and stokes matrices, Expositiones Mathematicae, vol.19, issue.3, pp.229-250, 2001.
DOI : 10.1016/S0723-0869(01)80003-7

B. Malgrange, La classification des connexionsirrégulì eresàeresà une variable, Mathematics and physics, pp.381-399, 1979.

B. Malgrange, Fourier transform and differential equations In Recent developments in quantum mechanics (Poiana Bra¸sovBra¸sov, Math. Phys. Stud, vol.12, pp.33-48, 1989.

B. Malgrange, Sommation des séries divergentes, Exposition. Math, vol.13, issue.2-3, pp.163-222, 1995.

R. Loday-richaud, Resurgence for level-one linear diff. systems 57

J. Martinet and J. Ramis, Elementary acceleration and multisummability. I. Ann, Inst. H. Poincaré Phys. Théor, vol.54, issue.4, pp.331-401, 1991.

J. Ramis and J. Martinet, Théorie de Galois différentielle et resommation, Computer algebra and differential equations, pp.117-214, 1990.

J. Ramis, Théorèmes d'indices Gevrey pour leséquationsleséquations différentielles ordinaires, Mem. Amer. Math. Soc, vol.48, issue.296, p.95, 1984.

J. Ramis, Phénomène de Stokes et resommation, C. R. Acad. Sci. Paris Sér. I Math, vol.301, issue.4, pp.99-102, 1985.

J. Ramis, Confluence et résurgence, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.36, issue.3, pp.703-716, 1989.

P. Remy, Résurgence des systèmes différentiels linéaires et calcul des matrices de Stokes, pp.1-408, 2007.

D. Sauzin, Resurgent functions and splitting problems, RIMS Kokyuroku, vol.1493, pp.48-117, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00150994

Y. Sibuya, Stokes phenomena, Bulletin of the American Mathematical Society, vol.83, issue.5, pp.1075-1077, 1977.
DOI : 10.1090/S0002-9904-1977-14391-7

Y. Sibuya, Linear differential equations in the complex domain: problems of analytic continuation, volume 82 of Translations of Mathematical Monographs, 1990.

H. L. Turrittin, Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point, Acta Mathematica, vol.93, issue.0, pp.27-66, 1955.
DOI : 10.1007/BF02392519

M. Van, D. Put, and M. F. Singer, Galois theory of linear differential equations, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 2003.

R. Loday-richaud, Resurgence for level-one linear diff, p.58

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