Divergent Series, Summability and Resurgence I

Monodromy and Resurgence
1. Auflage 2016
ISBN: 978-3-319-28735-5
Verlag: Springer International Publishing

Buch, Englisch, Band 2153, 298 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 4861 g

Reihe: Lecture Notes in Mathematics

Providing an elementary introduction to analytic continuation and monodromy, the first part of this volume applies these notions to the local and global study of complex linear differential equations, their formal solutions at singular points, their monodromy and their differential Galois groups. The Riemann-Hilbert problem is discussed from Bolibrukh’s point of view.
The second part expounds 1-summability and Ecalle’s theory of resurgence under fairly general conditions. It contains numerous examples and presents an analysis of the singularities in the Borel plane via “alien calculus”, which provides a full description of the Stokes phenomenon for linear or non-linear differential or difference equations.
The first of a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists interested in geometric, algebraic or local analytic properties of dynamical systems. It includes useful exercises with solutions. The prerequisites are a working knowledge of elementary complex analysis and differential algebra.

Zielgruppe

Research

Autoren/Hrsg.

Sauzin, David

Mitschi, Claude

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

Preface.-Preface to the three volumes.- Part I:Monodromy in Linear Differential Equations.- 1 analytic continuation and monodromy.- Differential Galois Theory.- Inverse Problems.- The Riemann-Hilbert problem.- Part II: Introduction to 1-Summability and Resurgence.- 5 Borel-Laplace Summation.- Resurgent Functions and Alien Calculus.- the Resurgent Viewpoint on Holomorphic Tangent-to-Identity Germs.- Acknowledgements.- Index.