The Stokes phenomenon and some applications (Q2353216)

This paper reviews the transparent description of the Stokes phenomenon made possible by multisummation and some applications such as moduli spaces of linear differential equations, quantum differential equations and confluent generalized hypergeometric equations and isomonodromy, the Painlevé equations and Okamoto-Painlevé spaces. The theory of multisummation is the work of many mathematicians such as W. Balser, B. L. J. Braaksma, J. Ecalle, W. B. Jurkat, D. Lutz, M. Loday-Richaud, B. Malgrange, J. Martinet, J.-P. Ramis and Y. Sibuya. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for the third Painlevé equation is made explicit. It is shown that the monodromy identity, relating the topological monodromy and Stokes matrices, is useful for some quantum differential equations and for confluent generalized hypergeometric equations.