Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 036, 13 pages      arXiv:1501.05205      https://doi.org/10.3842/SIGMA.2015.036
Contribution to the Special Issue on Algebraic Methods in Dynamical Systems

The Stokes Phenomenon and Some Applications

Marius van der Put
University of Groningen, Department of Mathematics, P.O. Box 407, 9700 AK Groningen, The Netherlands

Received January 21, 2015, in final form April 21, 2015; Published online May 01, 2015

Abstract
Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a 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.

Key words: Stokes matrices; moduli space for linear connections; quantum differential equations; Painlevé equations.

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