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arXiv 1303.3603math.CAmath-phmath.MP
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第三类Painelv'e方程的Voros系数与参量Stokes现象

Voros coefficients of the third Painelv'e equation and parametric Stokes phenomena

Kohei Iwaki

摘要:

计算了第三类D6型Painleve方程(在[OKSO]意义下)的所有Voros系数,并讨论了形式跨级数解的参数Stokes现象.我们推导出连接公式的参数斯托克斯现象的假设下transseries解决方案的Borel求和。此外,我们还计算了附录D中D7型退化第三类Painleve方程的Voros系数。

英文摘要:

We compute all Voros coefficients of the third Painleve equation of the type D6 (in the sense of [OKSO]) and discuss the parametric Stokes phenomena occurring to formal transseries solutions. We derive connection formulas for parametric Stokes phenomena under an assumption for Borel summability of transseries solutions. Furthermore, we also compute the Voros coefficient of the degenerate third Painleve equation of the type D7 in Appendix D.

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