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arXiv · 2110.15320

Folding transformations for q-Painleve equations

M. Bershtein·A. Shchechkin
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Abstract

Folding transformation of the Painlevé equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painlevé equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the $q$-difference Painlevé equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painlevé equations through rational surfaces.

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M. Bershtein, A. Shchechkin. 2021-10-28. Folding transformations for q-Painleve equations. https://arxiv.org/abs/2110.15320

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