Generating function of monodromy symplectomorphism for \(2 \times 2\) Fuchsian systems and its WKB expansion. (English) Zbl 1531.34082
Summary: We study the WKB expansion of \(2\times 2\) system of linear differential equations with Fuchsian singularities. The main focus is on the generating function of the monodromy symplectomorphism which, according to a recent paper [M. Bertola and D. Korotkin, Commun. Math. Phys. 388, No. 1, 245–290 (2021; Zbl 1537.37078)], 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.
MSC:
| 34M60 | Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) |
| 34M55 | Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies |
| 53D22 | Canonical transformations in symplectic and contact geometry |
Citations:
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