Journal of Dynamical and Control Systems

, Volume 3, Issue 3, pp 433–448 | Cite as

On the confluence phenomenon for fuchsian equations

  • B. Yu. Sternin
  • V. E. Shatalov
Article

Abstract

In the paper we present a method of investigation of asymptotic behavior of solutions to parameter-dependent degenerate differential equations both with regular and irregular points of singularity. We examine the confluence phenomenon for such points, which is the process of the coincidence of different points at a certain value of the parameter. This examination is based on a resurgent representation of the corresponding solutions which also depends on the parameter. In particular, the confluence of the representations in question is considered.

1991 Mathematics Subject Classification

34A20 

Key words and phrases

Fuchsian differential equation complex domain asymptotic expansion confluence phenomenon 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • B. Yu. Sternin
    • 1
  • V. E. Shatalov
    • 1
  1. 1.Unversité de Nice-Sophia Antipolis, Laboratoire Jean-Alexandre DieudonnéMoscow State UniversityNiceFrance

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