Study of structures of singular phenomena via complex global analysis

我们得到了一类合流超几何系统的单调性的具体公式，它可以写成哈密顿形式。该方法可推广到更一般的方程组，并可用于研究不规则奇点附近的联结公式。该方法与Kam理论有一定的相似性。研究的另一个结果是证明了一类多维Fuchsian方程的奇异摄动形式解的Borel可和性。这一结果在一个变量的情况下得到了证明。利用上述方法，我们分析了具有进化效应的三种群的Lotoka Volterra系统的解析行为。

We have obtained the concrete formula of the monodromy of a certain confluent hypergeometric system which can be written in a Hamiltonian form. The method may be extended to more general system of equations and may be applied to the study of connection formulas near the irregular singular point. The method has some similarity to the so-called KAM theory.The other result of the research is the proof of the Borel summability of a singular perturbative formal solution of a certain a multi-dimensional Fuchsian equation. This results was proved in the case of one variable. Using the method in the above we have analyzed the analytic behavior of Lotoka Volterra system of three species with evolutional effect.