Exact and asymptotic solutions of systems with turning points

A system of linear ordinary differential equations with analytic coefficients and small parameters on the derivative is considered. In a neighborhood of a turning point a new representation is constructed for the exact solution of the system in the form of a multiphase series. It is proved that this series converges uniformly with respect to the parameter. An expression is obtained for the Stokes constant at the maximal exponential. Bibligraphy: 10 titles.