Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions

Details Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions

2003-09-30

arxiv.org/abs/nlin/0309078v3

Nonlinear Sciences

Exactly Solvable and Integrable Systems

37 pages, Two references are added and commented in the Introduction

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dessins d'Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-280331