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Saddle-point method and resurgent analysis. (English. Russian original) Zbl 0915.58067
Math. Notes 61, No. 2, 227-241 (1997); translation from Mat. Zametki 61, No. 2, 278-296 (1997).
Summary: 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.

37G99 Local and nonlocal bifurcation theory for dynamical systems
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