Marta Mazzocco

Stokes phenomenon as confluence of regular behaviour

We will describe a general procedure to obtain systems of ODE with irregular singularities as confluent limits of Fuchsian systems. We show how to pass from solutions with power-like behaviour which are analytic in disks, to solutions with exponential behaviour which are analytic in sectors and have divergent asymptotics. We explicitly calculate the Stokes matrices of the confluent system in terms of the monodromy data, specifically the connection matrices, of the original system around the merging singularities.