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Painleve I, Coverings of the Sphere and Belyi Functions
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.Comment: 33 pages, many figures. Version 2: minor corrections and minor
changes in the bibliograph