, Volume 228, Issue 1, pp 151-176

Transformations RS42(3) of the Ranks ≤ 4¶and Algebraic Solutions of the Sixth Painlevé Equation

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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 × 2 matrix Fuchsian ODEs with 3 singular points into analogous ODE with 4 singular points are classified.

Received: 17 August 2001 / Accepted: 14 February 2002