Divergent Series, Summability and Resurgence I
Springer International Publishing (Verlag)
978-3-319-28735-5 (ISBN)
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.
Preface.-Preface to the three volumes.- Part I:Monodromy in Linear Differential Equations.- 1 analytic continuation and monodromy.- Differential Galois Theory.- Inverse Problems.- The Riemann-Hilbert problem.- Part II: Introduction to 1-Summability and Resurgence.- 5 Borel-Laplace Summation.- Resurgent Functions and Alien Calculus.- the Resurgent Viewpoint on Holomorphic Tangent-to-Identity Germs.- Acknowledgements.- Index.
"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)
| Erscheinungsdatum | 21.06.2016 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | XXI, 298 p. 24 illus., 19 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | 34M30,30E15,30B40,34M03,34M40,37F10,34M35 • Difference and Functional Equations • Differential Galois groups • Divergent series • Dynamical Systems and Ergodic Theory • mathematics and statistics • Ordinary differential equations • Resurgence • Riemann-Hilbert problem • Sequences, Series, Summability • Topological Groups, Lie Groups |
| ISBN-10 | 3-319-28735-4 / 3319287354 |
| ISBN-13 | 978-3-319-28735-5 / 9783319287355 |
| Zustand | Neuware |
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