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<p>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 <i>n</i> = 3. We then interpret Jimbo’s asymptotic and monodromy formula from the viewpoint of the isomonodromy deformation with respect to irregular singularities.</p>

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A New Interpretation of Jimbo’s Formula for Painlevé VI

  • 期刊论文

  • 发表日期：

    2026年1月5日

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  • Zikang Wang,
  • Yuancheng Xie,
  • Xiaomeng Xu

摘要

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.