标题： 离散Painlevé I中的Stokes现象 显示英文标题

标题： Stokes Phenomena in Discrete Painlevé I

摘要： 在本研究中，我们考虑当自变量变得很大时，第一个离散Painlevé方程的渐近行为。通过使用渐近级数展开，我们识别出两种类型的解，在包含正实轴的复平面上的某些区域中没有极点。利用指数渐近技术，我们确定了这些解中存在的斯托克斯现象效应，从而确定了渐近级数表达式的有效区域。通过对斯托克斯线上切换行为的仔细分析，我们发现第一种类型的解是唯一定义的，而第二种类型包含两个自由参数，并且通过适当选择这些参数可以扩展有效区域。 显示英文摘要

摘要： In this study, we consider the asymptotic behaviour of the first discrete Painlev\{e} equation in the limit as the independent variable becomes large. Using an asymptotic series expansion, we identify two types of solutions which are pole-free within some sector of the complex plane containing the positive real axis. Using exponential asymptotic techniques, we determine the Stokes Phenomena effects present within these solutions, and hence the regions in which the asymptotic series expression is valid. From a careful analysis of the switching behaviour across Stokes lines, we find that the first type of solution is uniquely defined, while the second type contains two free parameters, and that the region of validity may be extended for appropriate choice of these parameters.