Naslov
Confluence of Singularities in Hypergeometric Systems

Autori
Klimeš, Martin

Izvornik
Funkcialaj Ekvacioj-Serio Internacia (0532-8721) 63 (2020), 2; 153-181

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
linear differential equations ; generalized hypergeometric equation ; confluence ; Stokes matrices ; monodromy

Sažetak
A system in a Birkhoff normal form with an irregular singularity of Poincare rank 1 at the origin and a regular singularity at infinity is dual through the Borel-Laplace transform to a system in an Okubo form. Schafke has showed that the Birkhoff system can also be obtained from the Okubo system by a simple limiting procedure. The Okubo system comes naturally with two kinds of mixed solution bases, both of which are shown to converge under the limit procedure to the canonical sectoral solutions of the limit Birkhoff system. We define Stokes matrices of the Okubo system as connection matrices between different branches of these mixed solution bases and use them to relate the monodromy matrices of the Okubo system to the usual Stokes matrices of the limit system at the irregular singularity. This is illustrated on the example of confluence in the generalized hypergeometric equation.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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