Mathematical Notes

, Volume 61, Issue 2, pp 227–241 | Cite as

Saddle-point method and resurgent analysis

  • B. Yu. Sternin
  • V. E. Shatalov


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.

Key words

resurgent functions saddle-point method resurgent equations alient derivatives Stokes lines bifurcation 


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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • B. Yu. Sternin
    • 1
  • V. E. Shatalov
    • 2
  1. 1.M. V. LomonosovMoscow State UniversityUSSR
  2. 2.Institute for Applied MathematicsRussian Academy of SciencesUSSR

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