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Divergent Series, Summability and Resurgence III

Resurgent Methods and the First Painlevé Equation

  • Eric Delabaere

Part of the Lecture Notes in Mathematics book series (LNM, volume 2155)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Eric Delabaere
    Pages 15-32
  3. Eric Delabaere
    Pages 69-98
  4. Eric Delabaere
    Pages 147-207
  5. Back Matter
    Pages 227-230

About this book

Introduction

The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called “bridge equation”, which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. 

The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1. 

Keywords

34Mxx,34M30,40Cxx,35Q15,34M50,30B40,30D05,37Fxx,37F99,34M55 Divergent Series Summability Resurgence First Painlevé Equation Riemann-Hilbert Problem

Authors and affiliations

  • Eric Delabaere
    • 1
  1. 1.Département de MathématiquesUniversité d'AngersAngersFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-29000-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-28999-1
  • Online ISBN 978-3-319-29000-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site