1207.4361 (Davide Masoero)

Painleve I, Coverings of the Sphere and Belyi Functions    [PDF]

Davide Masoero

The theory of poles of solutions of Painleve-I is equivalent to the Nevanlinna problem of constructing a meromorphic function ramified over five points - counting multiplicities - and without critical points. We construct such meromorphic functions as limit of rational ones. In the case of the tritronquee solution these rational functions are Belyi functions.

View original: http://arxiv.org/abs/1207.4361