Introduction to Stokes Structures [electronic resource] /by Claude Sabbah.
by Sabbah, Claude [author.]; SpringerLink (Online service).
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BookSeries: Lecture Notes in Mathematics: 2060Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : 2013.Description: XIV, 249 p. 14 illus., 1 illus. in color. online resource.ISBN: 9783642316951.Subject(s): Mathematics | Geometry, algebraic | Differential Equations | Differential equations, partial | Sequences (Mathematics) | Mathematics | Algebraic Geometry | Ordinary Differential Equations | Approximations and Expansions | Sequences, Series, Summability | Several Complex Variables and Analytic Spaces | Partial Differential EquationsDDC classification: 516.35 Online resources: Click here to access online
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Springer eBooksSummary: 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.
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| MAIN LIBRARY | QA564-609 (Browse shelf) | Available |
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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.
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