Generating Function of Monodromy Symplectomorphism for 2 × 2 Fuchsian Systems and Its WKB Expansion

Marco Bertola; Dmitry Korotkin; Fabrizio Del Monte

doi:10.15407/mag19.02.301

Generating Function of Monodromy Symplectomorphism for 2 × 2 Fuchsian Systems and Its WKB Expansion

Marco Bertola, Dmitry Korotkin, Fabrizio Del Monte

Research output: Contribution to journal › Article › peer-review

Abstract

We study the VKB development of a 2 × 2 system of linear differential equations with Fuchs singularities. The main attention is focused on the generating function of a monodromic symplectomorphism, which, according to recent work [10], is closely related to the Jimbo–Miva tau function. We calculate the first three terms of the VKB development of the generating function and establish its connection with Bergman's tau function.

Original language	English
Pages (from-to)	301-338
Number of pages	38
Journal	Journal of mathematical physics, analysis, geometry
Volume	19
Issue number	2
DOIs	https://doi.org/10.15407/mag19.02.301
Publication status	Published - 25 Mar 2023
Externally published	Yes

Keywords

Fuchs system
monodromy mapping
generating function
tau function
VKB development

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Cite this

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abstract = "We study the VKB development of a 2 × 2 system of linear differential equations with Fuchs singularities. The main attention is focused on the generating function of a monodromic symplectomorphism, which, according to recent work [10], is closely related to the Jimbo–Miva tau function. We calculate the first three terms of the VKB development of the generating function and establish its connection with Bergman's tau function.",

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AU - Korotkin, Dmitry

AU - Del Monte, Fabrizio

PY - 2023/3/25

Y1 - 2023/3/25

N2 - We study the VKB development of a 2 × 2 system of linear differential equations with Fuchs singularities. The main attention is focused on the generating function of a monodromic symplectomorphism, which, according to recent work [10], is closely related to the Jimbo–Miva tau function. We calculate the first three terms of the VKB development of the generating function and establish its connection with Bergman's tau function.

AB - We study the VKB development of a 2 × 2 system of linear differential equations with Fuchs singularities. The main attention is focused on the generating function of a monodromic symplectomorphism, which, according to recent work [10], is closely related to the Jimbo–Miva tau function. We calculate the first three terms of the VKB development of the generating function and establish its connection with Bergman's tau function.

KW - Fuchs system

KW - monodromy mapping

KW - generating function

KW - tau function

KW - VKB development

U2 - 10.15407/mag19.02.301

DO - 10.15407/mag19.02.301

M3 - Article

SN - 1812-9471

VL - 19

SP - 301

EP - 338

JO - Journal of mathematical physics, analysis, geometry

JF - Journal of mathematical physics, analysis, geometry

IS - 2

ER -

Generating Function of Monodromy Symplectomorphism for 2 × 2 Fuchsian Systems and Its WKB Expansion

Abstract

Keywords

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