Infinite Series in a History of Analysis: Stages up to the Verge of Summability, Hans-Heinrich K?¶rle

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

Автор: Loday-Richaud
Название: Divergent Series, Summability and Resurgence II
ISBN: 3319290746 ISBN-13(EAN): 9783319290744
Издательство: Springer
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Описание: Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations.The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided, which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya’s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations.This volume is the second in a series of three, entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes, it can be read independently.

Автор: Delabaere
Название: Divergent Series, Summability and Resurgence III
ISBN: 3319289993 ISBN-13(EAN): 9783319289991
Издательство: Springer
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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: Hussain Munir
Название: European Union. On the Verge of Global Political Leadership
ISBN: 9811028834 ISBN-13(EAN): 9789811028830
Издательство: Springer
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Описание: This book outlines the foreign and security policy of the European Union as envisaged under the Common Foreign and Security Policy (CFSP). Since establishing the CFSP in the 1990s, the European Union (EU) has showed its enthusiasm for global leadership, empowering European citizenship, and developing its international standing as an economic and political supranational organization. In particular, the book examines the EU’s peacekeeping and conflict resolution dynamics in order to analyze the political and security dimensions of the EU. It argues that, due to the loose collective foreign policy and inter-bloc dilemmas, the EU has failed to perform as an actor of substance in international politics. However, at the regional level, the EU’s peacekeeping efforts have enjoyed considerable success. The book further explains the dynamics of successful (regional) and unsuccessful (extra-regional) peacekeeping and conflict resolution efforts on the part of the EU with the help of a case study. The case study assesses two key hypotheses: that the stronger an EU member state’s collective Europeanization approach is, the higher the success of the EU is in inter-bloc disputes; and that the weaker an EU member state’s execution of the CFSP on international disputes is, the less successful the EU is in the context of international peacekeeping.