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Algebraic solutions of the sixth Painleve equation

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arxiv 0809.4873 v2 pith:OPHLLV64 submitted 2008-09-28 math.CA hep-thmath-phmath.MPnlin.SI

Algebraic solutions of the sixth Painleve equation

Oleg Lisovyy , Yuriy Tykhyy This is my paper
classification math.CA hep-thmath-phmath.MPnlin.SI
keywords algebraicequationpainlevesolutionsactionclassesclassifyconjugacy
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abstract

We describe all finite orbits of an action of the extended modular group $\bar{\Lambda}$ on conjugacy classes of SL(2,C)-triples. The result is used to classify all algebraic solutions of the general Painleve VI equation up to parameter equivalence.

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  1. Geometry of the Ising persistence problem and the universal Bonnet-Manin Painlev\'e VI distribution

    math-ph 2026-03 conditional novelty 7.0

    The full persistence distribution in 1D Ising coarsening equals a Pfaffian Fredholm determinant of the sech kernel and is controlled by a Painlevé VI equation that is the mean curvature of a Bonnet surface.