On the monodromy of the deformed cubic oscillator
Classical Analysis and ODEs
2022-02-08 v2 Algebraic Geometry
Abstract
We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlev{\'e} equation. We use the generalised monodromy map for this equation to give solutions to the infinite-dimensional Riemann-Hilbert problems arising from the Donaldson-Thomas theory of the A2 quiver. These are the first known solutions to such problems beyond the uncoupled case. The appendix by Davide Masoero contains a WKB analysis of the asymptotics of the monodromy map.
Keywords
Cite
@article{arxiv.2006.10648,
title = {On the monodromy of the deformed cubic oscillator},
author = {Tom Bridgeland and Davide Masoero},
journal= {arXiv preprint arXiv:2006.10648},
year = {2022}
}
Comments
68 pages. The appendix by the 2nd author. A few minor changes in this version