Divergent Series Summability And Resurgence Ii


Divergent Series Summability And Resurgence Ii
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Divergent Series Summability And Resurgence Ii


Divergent Series Summability And Resurgence Ii
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Author : Michèle Loday-Richaud
language : en
Publisher: Springer
Release Date : 2016-06-28

Divergent Series Summability And Resurgence Ii written by Michèle Loday-Richaud and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-28 with Mathematics categories.


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.



Divergent Series Summability And Resurgence I Iii


Divergent Series Summability And Resurgence I Iii
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Author : Eric Delabaere
language : en
Publisher: Springer
Release Date : 2017-09

Divergent Series Summability And Resurgence I Iii written by Eric Delabaere and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09 with Mathematics categories.


This three-volume work treats divergent series in one variable, especially those arising as solutions to complex ordinary differential or difference equations, and methods for extracting their analytic information. It provides a systematic construction, illustrated with examples, of the various theories of summability and the theory of resurgence developed since the 1980s. The Stokes phenomenon, for both linear and non-linear equations, plays an underlying and unifying role throughout the volumes. Applications presented include resurgent analyses of the First Painlevé equation and of the tangent-to-identity germs of diffeomorphisms of C, and links to differential Galois theory and the Riemann-Hilbert problem for linear differential equations. The volumes are aimed at graduate students, mathematicians in general, and theoretical physicists who are interested in the theories of monodromy, summability, and resurgence, as well as the current problems in the field.Although the three volumes are closely related, they have been organized to be read independently. The prerequisites are advanced calculus, especially holomorphic functions in one complex variable, and differential algebra. Moreover; the various themes are presented thoroughly step-by-step so as to be accessible to first-year graduate students in mathematics. This three-volume treatise should become a reference on summability and resurgence.



Divergent Series Summability And Resurgence I


Divergent Series Summability And Resurgence I
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Author : Claude Mitschi
language : en
Publisher: Springer
Release Date : 2016-08-27

Divergent Series Summability And Resurgence I written by Claude Mitschi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-27 with Mathematics categories.


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.



Divergent Series Summability And Resurgence


Divergent Series Summability And Resurgence
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Author :
language : en
Publisher:
Release Date : 2016

Divergent Series Summability And Resurgence written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.




Divergent Series Summability And Resurgence Iii


Divergent Series Summability And Resurgence Iii
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Author : Eric Delabaere
language : en
Publisher: Springer
Release Date : 2016-06-28

Divergent Series Summability And Resurgence Iii written by Eric Delabaere and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-28 with Mathematics categories.


The aim of this volume is two-fold. First, to show how the resurgent methods introduced in volume 1 can be applied efficiently in a non-linear setting; to this end further properties of the resurgence theory must be developed. Second, to analyze the fundamental example of the First Painlevé equation. The resurgent analysis of singularities is pushed all the way up to the so-called “bridge equation”, which concentrates all information about the non-linear Stokes phenomenon at infinity of the First Painlevé equation. The third in a series of three, entitled Divergent Series, Summability and Resurgence, this volume is aimed at graduate students, mathematicians and theoretical physicists who are interested in divergent power series and related problems, such as the Stokes phenomenon. The prerequisites are a working knowledge of complex analysis at the first-year graduate level and of the theory of resurgence, as presented in volume 1.



Complex Differential And Difference Equations


Complex Differential And Difference Equations
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Author : Galina Filipuk
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-11-18

Complex Differential And Difference Equations written by Galina Filipuk and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-18 with Mathematics categories.


With a balanced combination of longer survey articles and shorter, peer-reviewed research-level presentations on the topic of differential and difference equations on the complex domain, this edited volume presents an up-to-date overview of areas such as WKB analysis, summability, resurgence, formal solutions, integrability, and several algebraic aspects of differential and difference equations.



The Painlev Handbook


The Painlev Handbook
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Author : Robert Conte
language : en
Publisher: Springer Nature
Release Date : 2020-11-07

The Painlev Handbook written by Robert Conte and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-07 with Science categories.


This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painlevé test and shows how Painlevé analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schrödinger equation, the Korteweg-de Vries equation, Hénon-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic and quintic Ginzburg-Landau equations. Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic Ginzburg-Landau equations; a close look at physical problems involving the sixth Painlevé function; and an overview of new results since the book’s original publication with special focus on finite difference equations. The book features tutorials, appendices, and comprehensive references, and will appeal to graduate students and researchers in both mathematics and the physical sciences.



Integrability Quantization And Geometry I Integrable Systems


Integrability Quantization And Geometry I Integrable Systems
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Author : Sergey Novikov
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-04-12

Integrability Quantization And Geometry I Integrable Systems written by Sergey Novikov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-12 with Education categories.


This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.



Geometric Methods In Physics Xxxix


Geometric Methods In Physics Xxxix
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Author : Piotr Kielanowski
language : en
Publisher: Springer Nature
Release Date : 2023-07-21

Geometric Methods In Physics Xxxix written by Piotr Kielanowski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-21 with Science categories.


This volume collects papers based on lectures given at the XXXIX Workshop on Geometric Methods in Physics, held in Białystok, Poland in June 2022. These chapters provide readers an overview of cutting-edge research in geometry, analysis, and a wide variety of other areas. Specific topics include: Classical and quantum field theories Infinite-dimensional groups Integrable systems Lie groupoids and Lie algebroids Representation theory Geometric Methods in Physics XXXIX will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas.



Resurgence Physics And Numbers


Resurgence Physics And Numbers
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Author : Frédéric Fauvet
language : en
Publisher: Springer
Release Date : 2017-11-17

Resurgence Physics And Numbers written by Frédéric Fauvet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-17 with Science categories.


This book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 18-22, 2015. This meeting originally stemmed from the impressive upsurge of interest for Jean Ecalle's alien calculus in Physics, in the last years – a trend that has considerably developed since then. The volume contains both original research papers and surveys, by leading experts in the field, reflecting the themes that were tackled at this event: Stokes phenomenon and resurgence, in various mathematical and physical contexts but also related constructions in algebraic combinatorics and results concerning numbers, specifically multiple zetavalues.