@article{AFST_2005_6_14_1_71_0, author = {Trinh, Duc Tai}, title = {Coefficients de Stokes du mod\`ele cubique : point de vue de la r\'esurgence quantique}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {71--103}, publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques}, address = {Toulouse}, volume = {6e s{\'e}rie, 14}, number = {1}, year = {2005}, doi = {10.5802/afst.1088}, zbl = {1074.81022}, mrnumber = {2118034}, language = {fr}, url = {https://afst.centre-mersenne.org/item/AFST_2005_6_14_1_71_0/} }
Duc Tai Trinh. Coefficients de Stokes du modèle cubique : point de vue de la résurgence quantique. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 1, pp. 71-103. doi : 10.5802/afst.1088. https://afst.centre-mersenne.org/item/AFST_2005_6_14_1_71_0/
[1] Anharmonic oscillator , Phys. Rev. 184, p. 1231-1260 (1969 ). | MR 260323
, -[2] Hyperasymptotics, Proc. Roy. Soc. Lond. A, Vol 430, p. 653-668, (1990). | MR 1070081 | Zbl 0745.34052
, -[3] Hyperasymptotics for integrals with saddles, Proc. Roy. Soc. Lond. A, Vol 434, p. 657-675 (1991). | MR 1126872 | Zbl 0764.30031
, -[4] Entire functions, Academic Press Inc., New York, ( 1954). | MR 68627 | Zbl 0058.30201
-[5] Une introduction à la résurgence , Gaz. Math. No. 42, p. 36-64 (1989). | MR 1029893 | Zbl 0825.30006
-[6] Approche de la résurgence, Actualités mathématiques, Hermann, Paris (1993). | Zbl 0791.32001
, , -[7] Singular lagrangian manifolds and semi-classiscal analysis, Soumis.
-[8] Asymptotic expansions, Cambridge University Press (1965). | MR 168979 | Zbl 0123.26001
-[9] Un peu d'asymptotique, Pupé 28 , janvier 1997, Université de Nice-Sophia Antipolis , URA 168 J.A. Dieudonné.
-[10] 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] Exact semi-classical expansions for one dimensional quantum oscillators, Journal Math. Phys. 38, 12, p. 6126-6184 (1997). | MR 1483488 | Zbl 0896.34051
, , -[12] 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] 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] 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] Global asymptotics for multiple integrals with boundaries, Duke Math. J. 112, no. 2, p. 199-264 (2002). | MR 1894360 | Zbl 1060.30049
, -[16] Asymptotic expansions : their derivation and interpretation , Academic Press, Oxford (1973). | MR 499926 | Zbl 0279.41030
-[17] 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] Cinq applications des fonctions résurgentes , preprint 84T 62, Orsay (1984).
-[19] 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] Asymptotic methods for linear ordinary differential equations, Moscow: Nauka, (1983). | MR 732787 | Zbl 0538.34001
-[21] Ordinary Differential Equations in the Complex Domain, Wiley (1976). | Zbl 0343.34007
-[22] 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] 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] Sommation des séries divergentes, Expositiones Mathematicae 13, p. 163-222 (1995). | MR 1346201 | Zbl 0836.40004
-[25] Equations différentielles à coefficients polynomiaux, Progress in Mathematics, Volume 96, Birkhaüser, Basel (1991). | Zbl 0764.32001
-[26] Théorie de Galois différentielle et resommation, Computer Algebra and Differential Equations (E. Tournier ed.), Acad. Press (1984). | Zbl 0722.12007
, -[27] 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] Asymptotics and special functions, New York, Academic Press ( 1974). | MR 435697 | Zbl 0303.41035
-[29] Vanishing homologies and the n variable saddlepoint method , Proc. Symposia in Pure Math. 40, part 2 (1983). | MR 713258 | Zbl 0519.49026
-[30] 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] Fonctions résurgentes implicites, C. R. Acad. Sci. Paris, 309, Série I, p. 999-1001 (1989). | MR 1054521 | Zbl 0734.32001
-[32] 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] 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] 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] 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] 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] 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] Borel-Laplace transform and Asymptotic Theory (Introduction to Resurgent Analysis, CRC-Press, Boca Raton, Florida, USA (1995). | MR 1397029 | Zbl 0852.34001
, -[39] 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] On the Discontinuity of arbitrary constants which appear in divergent developments, Transactions of the Cambridge Philosophical Society, Vol.X, Part. I (1857).
-[41] Asymptotique et analyse spectrale de l'oscillateur cubique , Thèse, Université de Nice (2002).
-[42] On the Sturm-Liouville problem for the complex cubic oscillator, To appear in Asymptotic Analysis. | Zbl 02150934
-[43] 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] Résurgence quantique, Ann. Inst. Fourier 43, 5, p. 1509-1534 (1993). | Numdam | MR 1275207 | Zbl 0807.35105
-[45] Asymptotic expansions for ODE, Interscience pub. (1965).
-[46] Quantum field theory and critical phenomena, Oxford science publications ( 1989). | MR 1079938 | Zbl 0865.00014
). -