Authors:
- 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
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2153)
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Table of contents (7 chapters)
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Front Matter
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Monodromy in Linear Differential Equations
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Front Matter
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Introduction to 1-Summability and Resurgence
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Front Matter
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Back Matter
About this book
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
Authors and Affiliations
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Inst. de Recherche Mathématique Avancée, Université de Strasbourg et CNRS, Strasbourg Cedex, France
Claude Mitschi
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CNRS UMR 8028 -- IMCCE, Observatoire de Paris, Pisa, Italy
David Sauzin
Bibliographic Information
Book Title: Divergent Series, Summability and Resurgence I
Book Subtitle: Monodromy and Resurgence
Authors: Claude Mitschi, David Sauzin
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-28736-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-28735-5Published: 28 August 2016
eBook ISBN: 978-3-319-28736-2Published: 27 August 2016
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XXI, 298
Number of Illustrations: 5 b/w illustrations, 19 illustrations in colour
Topics: Ordinary Differential Equations, Sequences, Series, Summability, Difference and Functional Equations, Dynamical Systems and Ergodic Theory, Topological Groups, Lie Groups