Divergent Series, Summability and Resurgence II, Loday-Richaud

Автор: Delabaere
Название: Divergent Series, Summability and Resurgence III
ISBN: 3319289993 ISBN-13(EAN): 9783319289991
Издательство: Springer
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Цена: 6288.00 р.
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Описание: The aim of this volume is two-fold. First, to show howthe resurgent methods introduced in volume 1 can be applied efficiently in anon-linear setting; to this end further properties of the resurgence theorymust be developed. Second, to analyze the fundamental example of the FirstPainlev? equation. The resurgent analysis of singularities is pushed all theway up to the so-called “bridge equation”, which concentrates allinformation about the non-linear Stokes phenomenon at infinity of the First Painlev?equation. The third in a series of three, entitled Divergent Series, Summability andResurgence, this volume is aimed at graduate students, mathematicians andtheoretical physicists who are interested in divergent power series and relatedproblems, such as the Stokes phenomenon. The prerequisites are a workingknowledge of complex analysis at the first-year graduate level and of thetheory of resurgence, as presented in volume 1.

Автор: Mitschi
Название: Divergent Series, Summability and Resurgence I
ISBN: 3319287354 ISBN-13(EAN): 9783319287355
Издательство: Springer
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Цена: 6288.00 р.
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Описание: 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.