Divergent Series, Summability and Resurgence I

Monodromy and Resurgence
Buch | Softcover
XXI, 298 Seiten
2016 | 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-28735-5 (ISBN)

Lese- und Medienproben

Divergent Series, Summability and Resurgence I - Claude Mitschi, David Sauzin
64,19 inkl. MwSt
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.

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
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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