论文标题
在变形的立方振荡器的单轨道上
On the monodromy of the deformed cubic oscillator
论文作者
论文摘要
我们研究了称为变形的立方振荡器的二阶线性微分方程，其异源性变形受到第一个Painlev {é}方程的控制。我们使用该方程式使用广义的单型图来为A2颤动的Donaldson-Thomas理论引起的无限二维Riemann-Hilbert问题提供解决方案。这些是除未偶联的情况之外的第一个已知解决方案。 Davide Masoero的附录包含对单片图的渐近学的WKB分析。
We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlev{é} 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.
