Introduction to Stokes Structures

Claude Sabbah (Autor)

Buch | Softcover

XIV, 249 Seiten

2012 | 2013
Springer Berlin (Verlag)
978-3-642-31694-4 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 4.10.2012
• Reihe/Serie: Lecture Notes in Mathematics
• Zusatzinfo: XIV, 249 p. 14 illus., 1 illus. in color.
• Verlagsort: Berlin
• Sprache: englisch
• Maße: 155 x 235 mm
• Gewicht: 418 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: 34M40, 32C38, 35A27 • Meromorphic connection • Ordinary differential equations • Partial differential equations • real blowing-up • Stokes filtration • Stokes-perverse sheaf
• ISBN-10: 3-642-31694-8 / 3642316948
• ISBN-13: 978-3-642-31694-4 / 9783642316944
• Zustand: Neuware