Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlev\'e and Gauss Hypergeometric Functions
Exactly Solvable and Integrable Systems
2007-05-23 v3 Classical Analysis and ODEs
Abstract
We consider an application of Grothendieck's dessins d'enfants to the theory of the sixth Painlev\'e 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 deformation of the dessins d'enfants and show that one dimensional deformations are a useful tool for construction of algebraic the sixth Painlev\'e functions.
Keywords
Cite
@article{arxiv.nlin/0309078,
title = {Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlev\'e and Gauss Hypergeometric Functions},
author = {A. V. Kitaev},
journal= {arXiv preprint arXiv:nlin/0309078},
year = {2007}
}
Comments
37 pages, Two references are added and commented in the Introduction