Introduction to Stokes Structures

By Claude Sabbah

Subjects: Differential equations, Approximations and Expansions, Sequences, Series, Summability, Algebraic Geometry, Ordinary Differential Equations, Sequences (Mathematics), Mathematics, Several Complex Variables and Analytic Spaces, Partial Differential equations

Description: This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf.<br>This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.