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Mathematics - Algebra | Introduction to Stokes Structures

Introduction to Stokes Structures

Series: Lecture Notes in Mathematics, Vol. 2060

Sabbah, Claude

2013, XIV, 249 p. 14 illus., 1 illus. in color.

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  • A first part on the classical theory of linear differential equations in the complex domain revisited from a geometric view point. Original and new study of the Stokes phenomenon in higher dimension. Application to classical problems in distribution theory.
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.

Content Level » Research

Keywords » 34M40, 32C38, 35A27 - Meromorphic connection - Stokes filtration - Stokes-perverse sheaf - real blowing-up

Related subjects » Algebra - Analysis - Dynamical Systems & Differential Equations

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