Divergent Series, Summability and Resurgence I

Monodromy and Resurgence

  • Claude Mitschi
  • David Sauzin

Part of the Lecture Notes in Mathematics book series (LNM, volume 2153)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Monodromy in Linear Differential Equations

    1. Front Matter
      Pages 1-2
    2. Claude Mitschi
      Pages 3-23
    3. Claude Mitschi
      Pages 25-73
    4. Claude Mitschi
      Pages 75-86
    5. Claude Mitschi
      Pages 87-119
  3. Introduction to 1-Summability and Resurgence

    1. Front Matter
      Pages 121-122
    2. David Sauzin
      Pages 123-171
    3. David Sauzin
      Pages 173-271
  4. Back Matter
    Pages 295-298

About this book

Introduction

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.

Keywords

34M30,30E15,30B40,34M03,34M40,37F10,34M35 Divergent series Resurgence Riemann-Hilbert problem Differential Galois groups

Authors and affiliations

  • Claude Mitschi
    • 1
  • David Sauzin
    • 2
  1. 1.Inst. de Recherche Mathématique AvancéeUniversité de Strasbourg et CNRSStrasbourg CedexFrance
  2. 2.CNRS UMR 8028 -- IMCCEObservatoire de ParisPisaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-28736-2
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-28735-5
  • Online ISBN 978-3-319-28736-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book