Schlesinger transformations for algebraic Painlevé VI solutions
نویسندگان
چکیده
Various Schlesinger transformations can be combined with a direct pull-back of a hypergeometric 2×2 system to obtainRS 4 -pullback transformations to isomonodromic 2× 2 Fuchsian systems with 4 singularities. The corresponding Painlevé VI solutions are algebraic functions, possibly in different orbits under Okamoto transformations. This paper demonstrates a direct computation of Schlesinger transformations acting on several apparent singular points, and presents an algebraic procedure (via syzygies) of computing algebraic Painlevé VI solutions without deriving full RS-pullback transformations. 2000 Mathematics Subject Classification: 34M55, 33E17. Short title: RS-pullback transformations
منابع مشابه
Computation of RS-pullback transformations for algebraic Painlevé VI solutions
Algebraic solutions of the sixth Painlevé equation can be computed using pullback transformations of hypergeometric equations with respect to specially ramified rational coverings. In particular, as was noticed by the second author and Doran, some algebraic solutions can be constructed from a rational covering alone, without computation of the pullbacked Fuchsian equation. But the same covering...
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