Resurgent methods and the first Painlevé equation

Bibliographic Information

Resurgent methods and the first Painlevé equation

Eric Delabaere

(Lecture notes in mathematics, 2155 . Divergent series, summability and resurgence ; 3)

Springer, c2016

Available at  / 42 libraries

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Note

Includes bibliographical references and index

Description and Table of Contents

Description

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 Painleve 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 Painleve 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.

Table of Contents

Avant-Propos.- Preface to the three volumes.- Preface to this volume.- Some elements about ordinary differential equations.- The first Painleve equation.- Tritruncated solutions for the first Painleve equation.- A step beyond Borel-Laplace summability.- Transseries and formal integral for the first Painleve equation.- Truncated solutions for the first Painleve equation.- Supplements to resurgence theory.- Resurgent structure for the first Painleve equation.- Index.

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Related Books: 1-1 of 1

Details

  • NCID
    BB21689703
  • ISBN
    • 9783319289991
  • LCCN
    2016940058
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Switzerland
  • Pages/Volumes
    xxii, 230 p.
  • Size
    24 cm
  • Parent Bibliography ID
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