Grothendieck’s Dessins D’enfants, Their Deformations, and Algebraic Solutions of the Sixth Painlevé and Gauss Hypergeometric Equations
نویسنده
چکیده
Grothendieck’s dessins d’enfants are applied to the theory of the sixth Painlevé and Gauss hypergeometric functions, two classical special functions of isomonodromy type. It is shown that higher-order transformations and the Schwarz table for the Gauss hypergeometric function are closely related to some particular Bely̆ı functions. Moreover, deformations of the dessins d’enfants are introduced, and it is shown that one-dimensional deformations are a useful tool for construction of algebraic sixth Painlevé functions.
منابع مشابه
Dessins d’Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions
We consider an application of Grothendieck’s dessins d’enfants to the theory of the sixth Painlevé and Gauss hypergeometric functions: two classical special functions of the isomonodromy type. It is shown that, higher order transformations and the Schwarz table for the Gauss hypergeometric function are closely related with some particular Belyi functions. Moreover, we introduce a notion of defo...
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