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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeJan 5th 2021
    • (edited Jan 15th 2021)

    Some important references added, including recent geometric study

    • Leonid O. Chekhov, Marta Mazzocco, Vladimir N. Rubtsov, Painlevé monodromy manifolds, decorated character varieties, and cluster algebras, IMRN 24 (2017) 7639–7691 doi

    and a section of papers studying the mathematics of Painlevé equations and of Fuchsian j Γj_\Gamma-functions from model theoretic perspective (strongly minimal structures), including a new paper in Annals 2020.

    diff, v11, current

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeSep 30th 2022
    • (edited Oct 4th 2022)

    Painlevé VI is 2nd order nonlinear ODE governing the isomonodromic deformations of Fuchsian differential equations

    dfdz=(A 1z+A 2zt+A 3z1), \frac{d f}{d z} = \left(\frac{A_1}{z} + \frac{A_2}{z-t}+ \frac{A_3}{z-1}\right),

    where A isl 2(C)A_i\in sl_2(\mathbf{C}) and parameter tt varies through P 1\{0,1,}\mathbf{P}^1\backslash\{0,1,\infty\}.

    diff, v18, current