Introduction to Stokes Structures [electronic resource] / by Claude Sabbah.
Sabbah, Claude. author.
SpringerLink (Online service)
Mathematics.
Geometry, algebraic.
Differential Equations.
Differential equations, partial.
Sequences (Mathematics).
QA564-609
516.35 23
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.
2013
Text
XIV, 249 p. 14 illus., 1 illus. in color.
http://dx.doi.org/10.1007/978-3-642-31695-1
eng
Springer eBooks
Lecture Notes in Mathematics, 0075-8434 ; 2060
Lecture Notes in Mathematics, 0075-8434 ; 2060