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Lecture Notes in Mathematics

Divergent Series, Summability and Resurgence III

Resurgent Methods and the First Painlevé Equation

Authors: Delabaere, Eric

  • Features a thorough resurgent analysis of the celebrated non-linear differential equation Painlevé I
  • Includes new specialized results in the theory of resurgence
  • For the first time, higher order Stokes phenomena of Painlevé I are made explicit by means of the so-called bridge equation
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eBook 41,64 €
price for France (gross)
  • ISBN 978-3-319-29000-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 52,74 €
price for France (gross)
  • ISBN 978-3-319-28999-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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. 

Table of contents (8 chapters)

  • Some Elements about Ordinary Differential Equations

    Delabaere, Eric

    Pages 1-14

    Preview Buy Chapter 29,94 €
  • The First Painlevé Equation

    Delabaere, Eric

    Pages 15-32

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  • Tritruncated Solutions For The First Painlevé Equation

    Delabaere, Eric

    Pages 33-68

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  • A Step Beyond Borel-Laplace Summability

    Delabaere, Eric

    Pages 69-98

    Preview Buy Chapter 29,94 €
  • Transseries And Formal Integral For The First Painlevé Equation

    Delabaere, Eric

    Pages 99-128

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Buy this book

eBook 41,64 €
price for France (gross)
  • ISBN 978-3-319-29000-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 52,74 €
price for France (gross)
  • ISBN 978-3-319-28999-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Divergent Series, Summability and Resurgence III
Book Subtitle
Resurgent Methods and the First Painlevé Equation
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2155
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29000-3
DOI
10.1007/978-3-319-29000-3
Softcover ISBN
978-3-319-28999-1
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXII, 230
Number of Illustrations
21 b/w illustrations, 14 illustrations in colour
Topics