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Transformations ${RS}_4^2(3)$ of the Ranks $\leq4$ and Algebraic Solutions of the Sixth Painlevé Equation

F. V. Andreev·A. V. Kitaev
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Abstract

Compositions of rational transformations of independent variables of linear matrix ordinary differential equations (ODEs) with the Schlesinger transformations ($RS$-transformations) are used to construct algebraic solutions of the sixth Painlevé equation. $RS$-Transformations of the ranks 3 and 4 of $2\times2$ matrix Fuchsian ODEs with 3 singular points into analogous ODE with 4 singular points are classified.

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F. V. Andreev, A. V. Kitaev. 2001-07-31. Transformations ${RS}_4^2(3)$ of the Ranks $\leq4$ and Algebraic Solutions of the Sixth Painlevé Equation. https://doi.org/10.1007/s002200200653

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