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arXiv · 2211.16615

Generating function of monodromy symplectomorphism for $2\times 2$ Fuchsian systems and its WKB expansion

Marco Bertola·Fabrizio Del Monte·Dmitry Korotkin
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Abstract

We study the WKB expansion of $2\times 2$ system of linear differential equations with four fuchsian singularities. The main focus is on the generating function of the monodromy symplectomorphism which, according to a recent paper is closely related to the Jimbo-Miwa tau-function. We compute the first three terms of the WKB expansion of the generating function and establish the link to the Bergman tau-function.

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Marco Bertola, Fabrizio Del Monte, Dmitry Korotkin. 2022-11-29. Generating function of monodromy symplectomorphism for $2\times 2$ Fuchsian systems and its WKB expansion. https://arxiv.org/abs/2211.16615

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