论文标题
杆动力学和多个SLE的运动不可或缺（0）
Pole dynamics and an integral of motion for multiple SLE(0)
论文作者
论文摘要
我们描述了一类真实理性函数的真实轨迹的Loewner链，该函数的临界点位于真实线上。我们的主要结果是，理性函数的极点为控制驱动功能的动力系统提供了明确的公式。我们的公式提供了一种简单的方法，可以将有理函数类映射到二次方程式的非平凡系统中，并直接表明真实基因座中的曲线满足几何换向的功能并具有地球多键属性。这些结果是完全独立的，不依赖概率对象，但是利用了由共同域理论的思想激励的Loewner链的运动组成部分。我们还表明，驾驶功能的动力学是Calogero-Moserable Antegers系统的特殊情况，仅限于LAX矩阵雕刻的特定相位空间子序列。我们的方法补充了Peltola和Wang的最新结果，他们表明真正的轨迹是确定性的Kappa到多个SLE（Kappa）曲线的0限制。
We describe the Loewner chains of the real locus of a class of real rational functions whose critical points are on the real line. Our main result is that the poles of the rational function lead to explicit formulas for the dynamical system that governs the driving functions. Our formulas give a simple method for mapping the class of rational functions into solutions to a non-trivial system of quadratic equations, and for directly showing that the curves in the real locus satisfy geometric commutation and have the geodesic multichord property. These results are entirely self-contained and have no reliance on probabilistic objects, but make use of an integral of motion for the Loewner chain that is motivated by ideas from conformal field theory. We also show that the dynamics of the driving functions are a special case of the Calogero-Moser integrable system, restricted to a particular submanifold of phase space carved out by the Lax matrix. Our approach complements a recent result of Peltola and Wang, who showed that the real locus is the deterministic kappa to 0 limit of the multiple SLE(kappa) curves.
