Moduli Spaces for the Fifth Painlev\'e Equation
Classical Analysis and ODEs
2023-09-27 v2 Exactly Solvable and Integrable Systems
Abstract
Isomonodromy for the fifth Painlev\'e equation is studied in detail in the context of certain moduli spaces for connections, monodromy, the Riemann-Hilbert morphism, and Okamoto-Painlev\'e spaces. This involves explicit formulas for Stokes matrices and parabolic structures. The rank 4 Lax pair for , introduced by Noumi-Yamada et al., is shown to be induced by a natural fine moduli space of connections of rank 4. As a by-product one obtains a polynomial Hamiltonian for , equivalent to the one of Okamoto.
Cite
@article{arxiv.2107.07204,
title = {Moduli Spaces for the Fifth Painlev\'e Equation},
author = {Marius van der Put and Jaap Top},
journal= {arXiv preprint arXiv:2107.07204},
year = {2023}
}