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Complete coalescent diagram of the Painleve equations

Yousuke Ohyama·Shoji Okumura
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Abstract

We will revise Garnier-Okamoto's coalescent diagram of isomonodromic deformations and give a complete coalescent diagram. In our viewpoint, we have ten types of isomonodromic deformations and two of them give the same type of the Painlevé equation. We can naturally put the thirty-fourth Painleve equation in our diagram, which corresponds to the Flaschka-Newell form of the second Painlevé equation.

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Yousuke Ohyama, Shoji Okumura. 2006-01-25. Complete coalescent diagram of the Painleve equations. https://arxiv.org/abs/math/0601614

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