Introduction to Stokes Structures
Sabbah, Claude.
Introduction to Stokes Structures [electronic resource] / by Claude Sabbah. - XIV, 249 p. 14 illus., 1 illus. in color. online resource. - Lecture Notes in Mathematics, 2060 0075-8434 ; . - Lecture Notes in Mathematics, 2060 .
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.
9783642316951
10.1007/978-3-642-31695-1 doi
Geometry, algebraic.
Differential Equations.
Mathematics.
Sequences (Mathematics).
Differential equations, partial.
Algebraic Geometry.
Ordinary Differential Equations.
Approximations and Expansions.
Sequences, Series, Summability.
Several Complex Variables and Analytic Spaces.
Partial Differential Equations.
QA564-609
516.35
Introduction to Stokes Structures [electronic resource] / by Claude Sabbah. - XIV, 249 p. 14 illus., 1 illus. in color. online resource. - Lecture Notes in Mathematics, 2060 0075-8434 ; . - Lecture Notes in Mathematics, 2060 .
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.
9783642316951
10.1007/978-3-642-31695-1 doi
Geometry, algebraic.
Differential Equations.
Mathematics.
Sequences (Mathematics).
Differential equations, partial.
Algebraic Geometry.
Ordinary Differential Equations.
Approximations and Expansions.
Sequences, Series, Summability.
Several Complex Variables and Analytic Spaces.
Partial Differential Equations.
QA564-609
516.35