Asymptotic analysis on the Painleve equations and monodromy problems

点击翻译按钮获取中文摘要

We study special solutions of the q-Painleve equations. In the case| q|=1, the first and the second q-Painleve equation has convergent solutions around the infinity. If q is a root of unity, they are represented by hypergeometric functions. We gave a coalescent diagram for q-hypergeometric functions and we obtain seven q-difference linear equations. For classical Painleve equations, we are studying convergence of asymptotic expansions. We also studied that monodromy evolving deformations for irregular singular cases.