关于Heine-Stieltjes多项式和Van Vleck多项式的渐近性
On asymptotic behavior of Heine-Stieltjes and Van Vleck polynomials
摘要：
研究了一类二阶复多项式系数微分方程的Heine-Stieltjes多项式-多项式解的强渐近性。该解决方案给出的关键措施（鞍点的加权对数能量的平面上），这是密切相关的二次微分与封闭的轨迹在平面上。本文是[arXiv：0902.0193]中开始的研究的延续。然而，这里的出发点是WKB方法，它允许获得强渐近性。
英文摘要：
We investigate the strong asymptotics of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. The solution is given in terms of critical measures (saddle points of the weighted logarithmic energy on the plane), that are tightly related to quadratic differentials with closed trajectories on the plane. The paper is a continuation of the research initiated in [arXiv:0902.0193]. However, the starting point here is the WKB method, which allows to obtain the strong asymptotics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
