[1] Bender (C.M. ) , Wu (T.T. ). - Anharmonic oscillator , Phys. Rev. 184, p. 1231-1260 (1969 ). | MR 260323

[2] Berry (M.V. ), Howls (C.J.). - Hyperasymptotics, Proc. Roy. Soc. Lond. A, Vol 430, p. 653-668, (1990). | MR 1070081 | Zbl 0745.34052

[3] Berry (M.V. ), Howls (C.J.). - Hyperasymptotics for integrals with saddles, Proc. Roy. Soc. Lond. A, Vol 434, p. 657-675 (1991). | MR 1126872 | Zbl 0764.30031

[4] Boas (R. Ph. ) Jr.. - Entire functions, Academic Press Inc., New York, ( 1954). | MR 68627 | Zbl 0058.30201

[5] Candelpergher ( B.). - Une introduction à la résurgence , Gaz. Math. No. 42, p. 36-64 (1989). | MR 1029893 | Zbl 0825.30006

[6] Candelpergher ( B.), Nosmas (C.), Pham (F.). - Approche de la résurgence, Actualités mathématiques, Hermann, Paris (1993). | Zbl 0791.32001

[7] Colin De Verdière ( Y.). - Singular lagrangian manifolds and semi-classiscal analysis, Soumis.

[8] Copson (E.T. ). - Asymptotic expansions, Cambridge University Press (1965). | MR 168979 | Zbl 0123.26001

[9] Delabaere ( E. ). - Un peu d'asymptotique, Pupé 28 , janvier 1997, Université de Nice-Sophia Antipolis , URA 168 J.A. Dieudonné.

[10] Delabaere ( E.), Dillinger (H.), Pham (F.). - Résurgence de Voros et périodes des courbes hyperelliptiques, Annales de l'Institut Fourier, Vol 43, Fasc. 1, p. 163-199 (1993). | Numdam | MR 1209700 | Zbl 0766.34032

[11] Delabaere ( E.), Dillinger (H.), Pham (F.). - Exact semi-classical expansions for one dimensional quantum oscillators, Journal Math. Phys. 38, 12, p. 6126-6184 (1997). | MR 1483488 | Zbl 0896.34051

[12] Delabaere ( E.), Pham (F.). - Resurgent methods in semi-classical asymptotics, Ann. Inst. Henri Poincaré, Sect. A, Vol. 71, No 1, p. 1-94 (1999). | Numdam | MR 1704654 | Zbl 0977.34053

[13] Delabaere ( E. ). - Introduction to the Ecalle theory , In E. Tournier, editor, Computer Algebra and Differential Equations, number 193, London Math. Soc., Lecture Note Series, Cambridge University Press, p. 59-102 (1994). | MR 1278057 | Zbl 0805.40007

[14] Delabaere ( E. ), Howls (C.J.). - Hyperasymptotics for multidimensional Laplace integrals with boundaries, Toward the exact WKB analysis of differential equations, linear or non-linear (Kyoto, 1998), 119, p. 145-163, Kyoto Univ. Press, Kyoto (2000). | MR 1770289 | Zbl 0998.58014

[15] Delabaere ( E.), Howls (C.J.). - Global asymptotics for multiple integrals with boundaries, Duke Math. J. 112, no. 2, p. 199-264 (2002). | MR 1894360 | Zbl 1060.30049

[16] Dingle (R.B. ). - Asymptotic expansions : their derivation and interpretation , Academic Press, Oxford (1973). | MR 499926 | Zbl 0279.41030

[17] Ecalle (J. ). - Les fonctions résurgentes, • Les algèbres de fonctions résurgentes, Publ. Math. D'Orsay , Université Paris-Sud, 1981.05 ( 1981 ). | Zbl 0499.30034

• Les fonctions résurgentes appliquées à l'itération, Publ. Math. D'Orsay, Université Paris-Sud, 1981.06 (1981). | Zbl 0499.30035

• L'équation du pont et la classification analytique des objets locaux , Publ. Math. D'Orsay, Université Paris-Sud , 1985.05 (1985). | MR 852210 | Zbl 0602.30029

[18] Ecalle (J. ). - Cinq applications des fonctions résurgentes , preprint 84T 62, Orsay (1984).

[19] Ecalle (J. ). - Weighted products and parametric resurgence, « Analyse algébrique des perturbations singulières I : Méthodes résurgentes », Travaux en cours, Hermann, Paris, p. 7-49 (1994). | Zbl 0834.34067

[20] Fedoryuk ( M.V. ). - Asymptotic methods for linear ordinary differential equations, Moscow: Nauka, (1983). | MR 732787 | Zbl 0538.34001

[21] Hille (E.). - Ordinary Differential Equations in the Complex Domain, Wiley (1976). | Zbl 0343.34007

[22] Jidoumou ( A.O.). - Modèles de Résurgence paramétrique (fonctions d'Airy et cylindro-paraboliques, J. Math. Pures et Appl., 73, 2, p. 111-190 (1994). | Zbl 0867.34046

[23] Loday-Richaud ( M.). - Solutions formelles des systèmes différentiels linéaires méromorphes et sommation, Exposition. Math. 13, no. 2-3, p. 116-162 (1995). | MR 1346200 | Zbl 0831.34002

[24] Malgrange ( B.). - Sommation des séries divergentes, Expositiones Mathematicae 13, p. 163-222 (1995). | MR 1346201 | Zbl 0836.40004

[25] Malgrange ( B.). - Equations différentielles à coefficients polynomiaux, Progress in Mathematics, Volume 96, Birkhaüser, Basel (1991). | Zbl 0764.32001

[26] Martinet ( J. ) , Ramis ( J.P.). - Théorie de Galois différentielle et resommation, Computer Algebra and Differential Equations (E. Tournier ed.), Acad. Press (1984). | Zbl 0722.12007

[27] Mezincescu ( G.A.). - Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant , J. Phys. A. 33 ( 2000). | MR 1792668 | Zbl 0973.34070

[28] Olver (F.W.J. ). - Asymptotics and special functions, New York, Academic Press ( 1974). | MR 435697 | Zbl 0303.41035

[29] Pham (F.). - Vanishing homologies and the n variable saddlepoint method , Proc. Symposia in Pure Math. 40, part 2 (1983). | MR 713258 | Zbl 0519.49026

[30] Pham (F.). - Resurgence, Quantized canonical transformations and multiinstanton expansions, in Algebraic Analysis II, vol. in honor of M.Sato, R.I.M.S. Kyoto, Kashiwara Kawai ed., Acad. Press, p. 699-726 (1988). | MR 992490 | Zbl 0686.58032

[31] Pham (F.). - Fonctions résurgentes implicites, C. R. Acad. Sci. Paris, 309, Série I, p. 999-1001 (1989). | MR 1054521 | Zbl 0734.32001

[32] Pham (F.). - Variétés lagrangiennes complexes et fonctions résurgentes, Actes du séminaire franco-viêtnamien « Analyse pluri-complexe et topologie des singularités », Math. J. Viêt. Math. Soc. , p. 97-130 (1995).

[33] Pham (F.). - Confluence of turning points in exact WKB analysis, The Stokes phenomenon and Hilbert's 16th problem (Groningen, 1995, p. 215-235, World Sci. Publishing, River Edge, NJ (1996). | MR 1443695 | Zbl 0857.34057

[34] Pham (F.). - Multiple turning points in exact WKB analysis (variations on a theme of Stokes), Toward the exact WKB analysis of differential equations linear or non-linear (C.Howls, T.Kawai, Y.Takei ed.), Kyoto University Press (2000), p. 71-85. | MR 1770284 | Zbl 1017.34091

[35] Ramis (J.P. ). - Séries divergentes et théories asymptotiques , Suppl. au bulletin de la SMF. Panoramas et Synthèses. v. 121. Paris : Société Mathématique de France ( 1993). | MR 1272100 | Zbl 0830.34045

[36] Ramis (J.P. ), Sibuya (Y.). - A new proof of multisummability of formal solutions of nonlinear meromorphic differential equations, Ann. Inst. Fourier (Grenoble)44, no. 3, p. 811-848 (1994). | Numdam | MR 1303885 | Zbl 0812.34005

[37] Sibuya (Y. ). - Global Theory of a Second Order Linear Differential Equation with a Polynomial Coefficient, Mathematics Studies 18, North-Holland Publishing Company (1975). | MR 486867 | Zbl 0322.34006

[38] Sternin (B. ) , Shatalov ( V.). - Borel-Laplace transform and Asymptotic Theory (Introduction to Resurgent Analysis, CRC-Press, Boca Raton, Florida, USA (1995). | MR 1397029 | Zbl 0852.34001

[39] Shin (K.C. ). - On the reality of the eigenvalues for a class of PT-symmetric oscillators, Comm. Math. Phys. 229 (2002), n°3, p. 543-564. | Zbl 1017.34083

[40] Stokes (G.G. ). - On the Discontinuity of arbitrary constants which appear in divergent developments, Transactions of the Cambridge Philosophical Society, Vol.X, Part. I (1857).

[41] Trinh (D.T. ). - Asymptotique et analyse spectrale de l'oscillateur cubique , Thèse, Université de Nice (2002).

[42] Trinh (D.T. ). - On the Sturm-Liouville problem for the complex cubic oscillator, To appear in Asymptotic Analysis. | Zbl 02150934

[43] Voros (A. ). - The return of the quartic oscillator. The complex WKB method, Ann. Inst. H. Poincaré, Physique Théorique, 39, p. 211-338 (1983). | Numdam | MR 729194 | Zbl 0526.34046

[44] Voros (A. ). - Résurgence quantique, Ann. Inst. Fourier 43, 5, p. 1509-1534 (1993). | Numdam | MR 1275207 | Zbl 0807.35105

[45] Wasow (W.). - Asymptotic expansions for ODE, Interscience pub. (1965).

[46] Zinn-Justin ( J.). - Quantum field theory and critical phenomena, Oxford science publications ( 1989). | MR 1079938 | Zbl 0865.00014