A New Interpretation of Jimbo’s Formula for Painlevé VI

Abstract

In this paper, we first give a new interpretation of Jimbo’s boundary condition for the generic Painlevé VI transcendents, as the shrinking phenomenon in long time behavior of the Jimbo–Miwa–Mori–Sato equation with rank n = 3. We then interpret Jimbo’s asymptotic and monodromy formula from the viewpoint of the isomonodromy deformation with respect to irregular singularities.

Keywords

Isomonodromy equations / Painlevé VI equations / irregular singularities / Stokes matrices / 34M35 / 34M40 / 34M55

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