Introduction to Stokes Structures
Nonfiction, Science & Nature, Mathematics, Differential Equations, Geometry
| Author: | Claude Sabbah | ISBN: | 9783642316951 |
| Publisher: | Springer Berlin Heidelberg | Publication: | October 3, 2012 |
| Imprint: | Springer | Language: | English |
| Author: | Claude Sabbah |
| ISBN: | 9783642316951 |
| Publisher: | Springer Berlin Heidelberg |
| Publication: | October 3, 2012 |
| Imprint: | Springer |
| Language: | English |
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.
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.
