Applied Mathematics Seminar

We study the global analytic properties of the solutions of Painlev\'e VI equation. Painlev\'e VI equation is a second order nonlinear ordinary differential equation in the complex variable $x$, depending on four parameters $\alpha,\beta,\gamma,\delta\in{\bf C}$. Its solutions define some new special functions called {\it Painlev\'e VI transcendents.} We try to find all the values of the parameters $(\alpha,\beta,\gamma,\delta)$ such that there exist particular solutions $y(x;c_1,c_2)$, determined by the integration constants $(c_1,c_2)$, that can be expressed via classical functions.