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arXiv · 2401.16043

A new interpretation of Jimbo's formula for Painlev\'e VI

Zikang Wang·Yuancheng Xie·Xiaomeng Xu
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Abstract

In this paper, we first give a new interpretation of Jimbo's boundary condition for the generic Painlev\'e VI transcendents, as the shrinking phenomenon in long time behaviour of the Jimbo-Miwa-Mori-Sato equation with rank $n=3$. We then interpret Jimbo's monodromy formula from the viewpoint of the isomonodromy deformation with respect to irregular singularities.

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Zikang Wang, Yuancheng Xie, Xiaomeng Xu. 2024-01-29. A new interpretation of Jimbo's formula for Painlev\'e VI. https://arxiv.org/abs/2401.16043

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