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Autor: Claude Mitschi
ISBN-13: 9783319287355
Einband: Book
Seiten: 298
Gewicht: 507 g
Format: 236x157x20 mm
Sprache: Englisch

Divergent Series, Summability and Resurgence I

2153, Lecture Notes in Mathematics
Monodromy and Resurgence
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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.
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All notions are motivated and illustrated by numerous examples and applications
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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.

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Autor: Claude Mitschi
ISBN-13 :: 9783319287355
ISBN: 3319287354
Erscheinungsjahr: 25.09.2016
Verlag: Springer-Verlag GmbH
Gewicht: 507g
Seiten: 298
Sprache: Englisch
Sonstiges: Taschenbuch, 236x157x20 mm, Bibliographie