Geodesic
Saddle-point method and resurgent analysis
Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 278-296.

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The topological part of the theory of the parameter-dependent Laplace integral is known to consist of two stages. At the first stage, the integration contour is reduced to a sum of paths of steepest descent for some value of the parameter. At the second stage, this decomposition (and hence the asymptotic expansion of the integral) is continued to all other parameter values. In the present paper, the second stage is studied with the help of resurgent analysis techniques. 
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B. Yu. Sternin; V. E. Shatalov. Saddle-point method and resurgent analysis. Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 278-296. http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a9/

[1] Écalle J., Les Fonctions Résurgentes, I, II, III, Publ. Mathématiques d'Orsay, Paris, 1981–1985

[2] Candelpergher B., Nosmas J. C., Pham F., Approche de la Résurgence, Hermann, Paris, 1993 | Zbl

[3] Sternin B., Shatalov V., “On a notion of resurgent function of several variables”, Math. Nachr., 171 (1995), 283–301 | DOI | MR | Zbl

[4] Sternin B., Shatalov V., Borel–Laplace Transform and Asymptotic Theory, CRC Press, Florida, 1995

[5] Berry M. V., Howls C. J., “Hyperasymptotics for integrals with saddles”, Proc. Roy. Soc. London. Ser. A, 443 (1991), 657–675 | MR

[6] Malgrange B., “Méthode de la phase stationnaire et sommation de Borel”, Complex Analysis. Microlocal Calculus and Relativistic Quantum Theory, Lecture Notes in Phys., 126, Springer-Verlag, Berlin–Heidelberg, 1980 | MR

[7] Pham F., “Vanishing homologies and the $n$ variable saddlepoint method”, Part 2, Proc. Sympos. Pure Math., 40, AMS, Providence, 1983, 319–333

[8] Sternin B., Shatalov V., Saddle Point Method and Resurgent Analysis, Preprint No. 95–69, Max-Planck-Institut für Mathematik, Bohn, 1995

[9] Sternin B., Shatalov V., Differential Equations on Complex Manifolds, Kluwer Acad. Publ., Dordrecht, 1994 | Zbl

[10] Fedoryuk M. V., Metod perevala, Nauka, M., 1977

[11] Tougeron J.-C., An introduction to the theory of Gevrey expansions and to Borel–Laplace transform with some applications, Preprint, Univ. of Toronto, Canada, 1990

[12] Lefschetz S., L'analysis Situs et la Géométrie Algébrique, Gauthier-Villars, Paris, 1924

[13] Delabaere E., “Introduction to the Écalle theory”, Computer Algebra and Differential Equations, London Math. Soc. Lecture Note Ser., 193, ed. E. Tournier, Univ. Press, Cambridge, 1994, 59–102 | MR