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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Some important references added, including recent geometric study
and a section of papers studying the mathematics of Painlevé equations and of Fuchsian $j_\Gamma$-functions from model theoretic perspective (strongly minimal structures), including a new paper in Annals 2020.
Painlevé VI is 2nd order nonlinear ODE governing the isomonodromic deformations of Fuchsian differential equations
$\frac{d f}{d z} = \left(\frac{A_1}{z} + \frac{A_2}{z-t}+ \frac{A_3}{z-1}\right),$where $A_i\in sl_2(\mathbf{C})$ and parameter $t$ varies through $\mathbf{P}^1\backslash\{0,1,\infty\}$.
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