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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. 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.

Differential equations, Linear --- Functions of complex variables --- Sheaf theory --- D-modules --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Calculus --- Differential equations, Linear. --- Stokes' theorem. --- Linear differential equations --- Mathematics. --- Algebraic geometry. --- Approximation theory. --- Differential equations. --- Partial differential equations. --- Sequences (Mathematics). --- Functions of complex variables. --- Algebraic Geometry. --- Ordinary Differential Equations. --- Approximations and Expansions. --- Sequences, Series, Summability. --- Several Complex Variables and Analytic Spaces. --- Partial Differential Equations. --- Linear systems --- Integrals --- Vector valued functions --- Geometry, algebraic. --- Differential Equations. --- Differential equations, partial. --- Partial differential equations --- Mathematical sequences --- Numerical sequences --- Algebra --- Math --- Science --- 517.91 Differential equations --- Differential equations --- Algebraic geometry --- Complex variables --- Elliptic functions --- Functions of real variables --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems