On the connection problem for Painlev\'e I
Exactly Solvable and Integrable Systems
2017-05-30 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
We study the dependence of the tau function of Painlev\'e I equation on the generalized monodromy of the associated linear problem. In particular, we compute connection constants relating the tau function asymptotics on five canonical rays at infinity. The result is expressed in terms of dilogarithms of cluster type coordinates on the space of Stokes data.
Cite
@article{arxiv.1612.08382,
title = {On the connection problem for Painlev\'e I},
author = {O. Lisovyy and J. Roussillon},
journal= {arXiv preprint arXiv:1612.08382},
year = {2017}
}
Comments
13 pages, 2 figures