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On the confluence phenomenon for Fuchsian equations. (English) Zbl 0943.34082
Summary: The authors present a method of investigation of the asymptotic behavior of solutions to parameter-dependent degenerate differential equations both with regular and irregular points of singularity. The confluence phenomenon for such points is examined, 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.

MSC:
34M37 Resurgence phenomena (MSC2000)
34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
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