Résurgence d'un thème de Huygens-Fresnel

 Access to full text

 Full (PDF)

1. [Ai] G. I. AIRY, On the Intensity of Light in the neighbourhood of a caustic, Trans. Camb. Phil. Soc., 6 (1838), 379-402. 
2. [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. Zbl0278.57010MR50 #8594
3. [Ar2] V. I. ARNOLD, Remarks on the method of stationary phase and Coxeter numbers, Usp. Mat. Nauk, 28, 5 (1973), 17-44. Zbl0291.40005MR53 #1635
4. [BB] R. BALIAN, C. BLOCH, Solution of the Schrödinger equation in terms of classical paths, Ann. of Physics, 85 (1974), 514-545. Zbl0281.35029MR55 #11840
5. [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. MR58 #8816
6. [BM] M. V. BERRY, K. E. MOUNT, Semiclassical approximations in wave mechanics, Rep. Progr. Phys., 35 (1972), 315-397. 
7. [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. 
8. [BU] M. V. BERRY, C. UPSTILL, Catastrophe Optics: Morphologies of Caustics and their Diffraction Patterns, Progress in Optics, 18 (1980), 258-346. 
9. [BW] M. BORN and E. WOLF, Principles of Optics, Pergamon Press, 1975. 
10. [CNP1] B. CANDELPERGER, C. NOSMAS et F. PHAM, Une approche de la résurgence (livre à paraître). 
11. [CNP2] B. CANDELPERGER, C. NOSMAS et F. PHAM, Résurgence et Développements semi-classiques (livre en préparation). 
12. [CFU] C. CHESTER, B. FRIEDMAN and F. URSELL, An Extension of the Method of Steepest Descent, Proc. Camb, Phil. Soc., 53 (1957), 599-611. Zbl0082.28601MR19,853a
13. [Di] R. B. DINGLE, Asymptotic Expansions : their derivation and interpretation, Acad. Press, 1973. Zbl0279.41030MR58 #17673
14. [Du] J. J. DUISTERMAAT, Oscillatory integrals, Lagrange immersions and unfolding of singularities, Comm. Pure and Applied Maths., 27 (1974), 207-281. Zbl0285.35010MR53 #9306
15. [E1] J. ECALLE, Les fonctions résurgentes (Publ. math. Université de Paris-Sud : en plusieurs tomes). Zbl0499.30034
16. [E2] J. ECALLE, Singularités irrégulières et résurgence multiple, in Cinq applications des fonctions résurgentes (preprint 84T 62, Orsay), 2-42. 
17. [Eg] I. V. EGOROV, On canonical transformations of pseudo-differential equations, Usp. Mat. Nauk, 24, 5 (1969), 235-236. Zbl0191.43802
18. [FM] M. V. FEDORIUK, V. P. MASLOV, Semi-classical Approximation in Quantum Mechanics, Reidel Publ. Company, 1981. Zbl0458.58001MR84k:58226
19. [GS] V. GUILLEMIN, S. STERNBERG, Geometric Asymptotics, A.M.S. Math. Surveys, 14 (1977). Zbl0364.53011MR58 #24404
20. [Ha] J. HARTHONG, La propagation des ondes, in Etudes sur la mécanique quantique (Astérisque, 111, 1984). 92-208. MR85i:81003
21. [Hö] L. HÖRMANDER, Fourier integral operators I, Acta Math., 127 (1971), 79-183. Zbl0212.46601MR52 #9299
22. [K] M. KASHIWARA, Microlocal calculus, in Mathematical problems in Theoretical Physics (Lecture Notes in Physics, 39, 1975). Zbl0355.34033MR58 #31298
23. [KK] M. KASHIWARA, T. KAWAI, On holonomic systems of microdifferential equations III, Publ. R.I.M.S., Kyoto Univ., 17, 3 (1981), 813-979. Zbl0505.58033MR83e:58085
24. [KKO] M. KASHIWARA, T. KAWAI, T. OSHIMA, A study of Feynman integrals by microdifferential equations, Commun. Math. Physics, 60 (1978), 97-130. Zbl0392.46025MR58 #24405
25. [Ma] V. MASLOV, Theory of perturbations and asymptotic methods (Moscow State University, 1965). 
26. [MG] S. C. MILLER and R. H. GOOD, Jr., A WKB-type Approximation to the Schrödinger Equation, Phys. Rev., 91, 1 (1953), 174-179. Zbl0050.22103
27. [Mi] TH. MILLER, Verallgemeinerte Airyfunktionen, Dissertation, Bonner Math. Schriften, 1988. Zbl0667.33009
28. [Pe] T. PEARCEY, The Structure of an Electromagnetic Field in the Neighbourhood of a Cusp of a Caustic, Phil. Mag., 37 (1946), 311-317. MR8,605d
29. [Ph1] F. PHAM, Caustiques, phase stationnaire, et microfonctions, Acta Mathematica Vietnamica, 2, 2 (1977), 35-101. Zbl0431.58018MR58 #22648
30. [Ph2] F. PHAM, Singularités des systèmes différentiels de Gauss-Manin, Progress in Math. 2, Birkhäuser (1980). Zbl0524.32015MR81h:32015
31. [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. 
32. [Ph4] F. PHAM, Transformées de Laplace des microsolutions de systèmes holonomes, L'enseignement mathématique, 30 (1984), 57-84. Zbl0578.58038MR86d:58112
33. [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. 
34. [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. Zbl0597.32012MR87h:32017
35. [Ph7] F. PHAM, Resurgence, Quantized canonical transformations and multi-instanton expansions, in Prospect in Algebraic Analysis, R.I.M.S. Kyoto (à paraître). Zbl0686.58032
36. [SKK] M. SATO, T. KAWAI, M. KASHIWARA, Microfunctions and pseudodifferential equations, Lecture Notes in Mathematics, 287 (1973), 265-529. Zbl0277.46039MR54 #8747
37. [V] A. VOROS, The return of the quartic oscillator (the complex WKB method), Ann. Inst. H. Poincaré, 29, 3 (1983), 211-338. Zbl0526.34046MR86m:81051
38. [W] C. WAGSCHAL, Problème de Cauchy ramifié, à caractéristiques multiples, holomorphes de multiplicité variable, J. Math. pures et appl., 62 (1983), 99-127. Zbl0545.35005MR85e:35008
39. [WW] E. WHITTAKER and G. WATSON, Modern Analysis, New York, The Macmillan Company, 1947. 

1. Nguyen Hu'u Du'c, Frédéric Pham, Germes de configurations legendriennes stables et fonctions d'Airy-Weber généralisées
2. B. Candelpergher, Jean-Claude Nosmas, Frédéric Pham, Premiers pas en calcul étranger
3. Carme Olivé, David Sauzin, Tere M. Seara, Resurgence in a Hamilton-Jacobi equation
4. Eric Delabaere, Frédéric Pham, Resurgent methods in semi-classical asymptotics
5. , Publications de Frédéric Pham