Résurgence d'un thème de Huygens-Fresnel
Publications Mathématiques de l'IHÉS, Volume 68  (1988), p. 77-90
@article{PMIHES_1988__68__77_0,
     author = {Pham, Fr\'ed\'eric},
     title = {R\'esurgence d'un th\`eme de Huygens-Fresnel},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {68},
     year = {1988},
     pages = {77-90},
     zbl = {0688.35093},
     mrnumber = {90g:58133},
     language = {fr},
     url = {http://www.numdam.org/item/PMIHES_1988__68__77_0}
}
Pham, Frédéric. Résurgence d'un thème de Huygens-Fresnel. Publications Mathématiques de l'IHÉS, Volume 68 (1988) , pp. 77-90. http://www.numdam.org/item/PMIHES_1988__68__77_0/

[Ai] G. I. Airy, On the Intensity of Light in the neighbourhood of a caustic, Trans. Camb. Phil. Soc., 6 (1838), 379-402.

[Ar1] V. I. Arnold, Integrals of rapidly oscillating functions and singularities of the projections of Lagrangean manifolds, Funct. Anal. and its Appl., 6, 3 (1972), 61-62. | MR 50 #8594 | Zbl 0278.57010

[Ar2] V. I. Arnold, Remarks on the method of stationary phase and Coxeter numbers, Usp. Mat. Nauk, 28, 5 (1973), 17-44. | MR 53 #1635 | Zbl 0291.40005

[BB] R. Balian, C. Bloch, Solution of the Schrödinger equation in terms of classical paths, Ann. of Physics, 85 (1974), 514-545. | MR 55 #11840 | Zbl 0281.35029

[Be] M. V. Berry, Cusped rainbows and incoherence effects in the rippling-mirror model for particle scattering from surfaces, J. Phys., A 8, 4 (1975), 566-584. | MR 58 #8816

[BM] M. V. Berry, K. E. Mount, Semiclassical approximations in wave mechanics, Rep. Progr. Phys., 35 (1972), 315-397.

[BNW] M. V. Berry, J. F. Nye and F. J. Wright, The Elliptic Umbilic Diffraction Catastrophe, Phil. Trans. Roy. Soc. London, A 291 (1979), 453-484.

[BU] M. V. Berry, C. Upstill, Catastrophe Optics: Morphologies of Caustics and their Diffraction Patterns, Progress in Optics, 18 (1980), 258-346.

[BW] M. Born and E. Wolf, Principles of Optics, Pergamon Press, 1975.

[CNP1] B. Candelperger, C. Nosmas et F. Pham, Une approche de la résurgence (livre à paraître).

[CNP2] B. Candelperger, C. Nosmas et F. Pham, Résurgence et Développements semi-classiques (livre en préparation).

[CFU] C. Chester, B. Friedman and F. Ursell, An Extension of the Method of Steepest Descent, Proc. Camb, Phil. Soc., 53 (1957), 599-611. | MR 19,853a | Zbl 0082.28601

[Di] R. B. Dingle, Asymptotic Expansions : their derivation and interpretation, Acad. Press, 1973. | MR 58 #17673 | Zbl 0279.41030

[Du] J. J. Duistermaat, Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure and Applied Maths., 27 (1974), 207-281. | MR 53 #9306 | Zbl 0285.35010

[E1] J. Ecalle, Les fonctions résurgentes (Publ. math. Université de Paris-Sud : en plusieurs tomes). | Zbl 0499.30034

[E2] J. Ecalle, Singularités irrégulières et résurgence multiple, in Cinq applications des fonctions résurgentes (preprint 84T 62, Orsay), 2-42.

[Eg] I. V. Egorov, On canonical transformations of pseudo-differential equations, Usp. Mat. Nauk, 24, 5 (1969), 235-236. | Zbl 0191.43802

[FM] M. V. Fedoriuk, V. P. Maslov, Semi-classical Approximation in Quantum Mechanics, Reidel Publ. Company, 1981. | MR 84k:58226 | Zbl 0458.58001

[GS] V. Guillemin, S. Sternberg, Geometric Asymptotics, A.M.S. Math. Surveys, 14 (1977). | MR 58 #24404 | Zbl 0364.53011

[Ha] J. Harthong, La propagation des ondes, in Etudes sur la mécanique quantique (Astérisque, 111, 1984). 92-208. | MR 85i:81003

[Hö] L. Hörmander, Fourier integral operators I, Acta Math., 127 (1971), 79-183. | MR 52 #9299 | Zbl 0212.46601

[K] M. Kashiwara, Microlocal calculus, in Mathematical problems in Theoretical Physics (Lecture Notes in Physics, 39, 1975). | MR 58 #31298 | Zbl 0355.34033

[KK] M. Kashiwara, T. Kawai, On holonomic systems of microdifferential equations III, Publ. R.I.M.S., Kyoto Univ., 17, 3 (1981), 813-979. | MR 83e:58085 | Zbl 0505.58033

[KKO] M. Kashiwara, T. Kawai, T. Oshima, A study of Feynman integrals by microdifferential equations, Commun. Math. Physics, 60 (1978), 97-130. | MR 58 #24405 | Zbl 0392.46025

[Ma] V. Maslov, Theory of perturbations and asymptotic methods (Moscow State University, 1965).

[MG] S. C. Miller and R. H. Good, Jr., A WKB-type Approximation to the Schrödinger Equation, Phys. Rev., 91, 1 (1953), 174-179. | Zbl 0050.22103

[Mi] Th. Miller, Verallgemeinerte Airyfunktionen, Dissertation, Bonner Math. Schriften, 1988. | Zbl 0667.33009

[Pe] T. Pearcey, The Structure of an Electromagnetic Field in the Neighbourhood of a Cusp of a Caustic, Phil. Mag., 37 (1946), 311-317. | MR 8,605d

[Ph1] F. Pham, Caustiques, phase stationnaire, et microfonctions, Acta Mathematica Vietnamica, 2, 2 (1977), 35-101. | MR 58 #22648 | Zbl 0431.58018

[Ph2] F. Pham, Singularités des systèmes différentiels de Gauss-Manin, Progress in Math. 2, Birkhäuser (1980). | MR 81h:32015 | Zbl 0524.32015

[Ph3] F. Pham, Calcul microdifférentiel complexe et méthode semi-classique, R.C.P. n° 25, vol. 32, I.R.M.A., Strasbourg, 1983, 59-72.

[Ph4] F. Pham, Transformées de Laplace des microsolutions de systèmes holonomes, L'enseignement mathématique, 30 (1984), 57-84. | MR 86d:58112 | Zbl 0578.58038

[Ph5] F. Pham, Exercice semi-classique, in Actes du colloque Méthodes semiclassiques en mécanique quantique, Publ. Univ. Nantes, Hellfer, Robert & Sjöstrand ed., 1985, 75-77.

[Ph6] F. Pham, La descente des cols par les onglets de Lefschetz, avec vues sur Gauss-Manin, in Systèmes différentiels et singularités, Astérisque, 130 (1985), 11-47. | MR 87h:32017 | Zbl 0597.32012

[Ph7] F. Pham, Resurgence, Quantized canonical transformations and multi-instanton expansions, in Prospect in Algebraic Analysis, R.I.M.S. Kyoto (à paraître). | Zbl 0686.58032

[SKK] M. Sato, T. Kawai, M. Kashiwara, Microfunctions and pseudodifferential equations, Lecture Notes in Mathematics, 287 (1973), 265-529. | MR 54 #8747 | Zbl 0277.46039

[V] A. Voros, The return of the quartic oscillator (the complex WKB method), Ann. Inst. H. Poincaré, 29, 3 (1983), 211-338. | Numdam | MR 86m:81051 | Zbl 0526.34046

[W] C. Wagschal, Problème de Cauchy ramifié, à caractéristiques multiples, holomorphes de multiplicité variable, J. Math. pures et appl., 62 (1983), 99-127. | MR 85e:35008 | Zbl 0545.35005

[WW] E. Whittaker and G. Watson, Modern Analysis, New York, The Macmillan Company, 1947.