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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     author = {B. Yu. Sternin and V. E. Shatalov},
     title = {Saddle-point method and resurgent analysis},
     journal = {Matemati\v{c}eskie zametki},
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     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a9/}
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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/