On some examples of identifying Painlevé equations using the geometry of the Okamoto space of initial conditions

Anton Dzhamay

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arXiv · 2508.12052

On some examples of identifying Painlevé equations using the geometry of the Okamoto space of initial conditions

Anton Dzhamay

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Abstract

In this short note we give two examples of using the algebro-geometric theory of Painlevé equations to solve the Painlevé identification problem. The equations that we consider were recently obtained by M. van der Put and J. Top in their study of a certain ansatz of isomonodromic deformations of linear ODEs. We provide explicit coordinate transformations identifying these examples with standard form of some Painlevé equations and also explicitly identify their Hamiltonians.

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Anton Dzhamay. 2025-08-16. On some examples of identifying Painlevé equations using the geometry of the Okamoto space of initial conditions. https://arxiv.org/abs/2508.12052

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