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Lecture Notes in Mathematics

Divergent Series, Summability and Resurgence I

Monodromy and Resurgence

Authors: Mitschi, Claude, Sauzin, David

  • Features an elementary, self-contained introduction to analytic differential Galois theory and the Riemann-Hilbert problem
  • Provides a foundation that will allow the reader to independently explore and understand the specialized literature in the field
  • Focuses on 1-summability and resurgence, with a view to nonlinear problems
  • For the first time, resurgence theory is introduced with great pedagogical care and the main proofs are given in full detail
  • All notions are motivated and illustrated by numerous examples and applications
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  • ISBN 978-3-319-28736-2
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Softcover $59.99
price for USA in USD
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About this book

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.

Reviews

“The book is the first of three independent books whose aim is to describe methods of the analytic theory of differential equations such as monodromy, analytic continuation, resurgence, summability etc. It is aimed at graduate students, mathematicians and theoretical physicists.” (Vladimir P. Kostov, zbMATH 1355.34003, 2017)


Table of contents (7 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-3-319-28736-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-28735-5
  • 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 I
Book Subtitle
Monodromy and Resurgence
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2153
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-28736-2
DOI
10.1007/978-3-319-28736-2
Softcover ISBN
978-3-319-28735-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXI, 298
Number of Illustrations and Tables
5 b/w illustrations, 19 illustrations in colour
Topics