Divergent Series Summability And Resurgence Ii

Author : Michèle Loday-Richaud
Publisher : Springer
Page : 272 pages
File Size : 49,9 Mb
Release : 2016-06-28
Category : Mathematics
ISBN : 9783319290751

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Divergent Series, Summability and Resurgence II by Michèle Loday-Richaud Pdf

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.

Author : Eric Delabaere
Publisher : Springer
Page : 230 pages
File Size : 47,5 Mb
Release : 2016-06-28
Category : Mathematics
ISBN : 9783319290003

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Divergent Series, Summability and Resurgence III by Eric Delabaere Pdf

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.

Author : Claude Mitschi,David Sauzin
Publisher : Springer
Page : 298 pages
File Size : 49,9 Mb
Release : 2016-08-27
Category : Mathematics
ISBN : 9783319287362

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Divergent Series, Summability and Resurgence I by Claude Mitschi,David Sauzin Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,9 Mb
Release : 2016
Category : Electronic
ISBN : OCLC:1076044697

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Divergent Series, Summability and Resurgence by Anonim Pdf

Author : Eric Delabaere,Michèle Loday-Richaud,Claude Mitschi,David Sauzin
Publisher : Springer
Page : 128 pages
File Size : 45,9 Mb
Release : 2017-09
Category : Mathematics
ISBN : 331959527X

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Divergent Series, Summability and Resurgence I-III by Eric Delabaere,Michèle Loday-Richaud,Claude Mitschi,David Sauzin Pdf

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.

Author : Galina Filipuk,Alberto Lastra,Sławomir Michalik,Yoshitsugu Takei,Henryk Żołądek
Publisher : Walter de Gruyter GmbH & Co KG
Page : 473 pages
File Size : 45,8 Mb
Release : 2019-11-18
Category : Mathematics
ISBN : 9783110611427

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Complex Differential and Difference Equations by Galina Filipuk,Alberto Lastra,Sławomir Michalik,Yoshitsugu Takei,Henryk Żołądek Pdf

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.

Author : Robert Conte,Micheline Musette
Publisher : Springer Nature
Page : 389 pages
File Size : 52,7 Mb
Release : 2020-11-07
Category : Science
ISBN : 9783030533403

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The Painlevé Handbook by Robert Conte,Micheline Musette Pdf

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.

Author : Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Publisher : American Mathematical Soc.
Page : 516 pages
File Size : 50,9 Mb
Release : 2021-04-12
Category : Education
ISBN : 9781470455910

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Integrability, Quantization, and Geometry: I. Integrable Systems by Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman Pdf

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.

Author : Piotr Kielanowski,Alina Dobrogowska,Gerald A. Goldin,Tomasz Goliński
Publisher : Springer Nature
Page : 345 pages
File Size : 52,5 Mb
Release : 2023-07-21
Category : Science
ISBN : 9783031302848

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Geometric Methods in Physics XXXIX by Piotr Kielanowski,Alina Dobrogowska,Gerald A. Goldin,Tomasz Goliński Pdf

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.

Author : Frédéric Fauvet,Dominique Manchon,Stefano Marmi,David Sauzin
Publisher : Springer
Page : 384 pages
File Size : 53,6 Mb
Release : 2017-11-17
Category : Science
ISBN : 9788876426131

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Resurgence, Physics and Numbers by Frédéric Fauvet,Dominique Manchon,Stefano Marmi,David Sauzin Pdf

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.

Author : Ahmed F. Zobaa,Shady H.E. Abdel Aleem,Ahmed M. Zobaa
Publisher : BoD – Books on Demand
Page : 120 pages
File Size : 51,9 Mb
Release : 2021-06-09
Category : Science
ISBN : 9781839687327

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Emerging Electric Machines by Ahmed F. Zobaa,Shady H.E. Abdel Aleem,Ahmed M. Zobaa Pdf

This book is an introduction to the concepts and developments of emerging electric machines, including advances, perspectives, and selected applications. It is a helpful tool for practicing engineers concerned with emerging electric machines and their challenges and potential uses. Chapters cover such topics as electric machines with axial magnetic flux, asynchronous machines with dual power supply, new designs for electrical machines, and more.

Author : Galina Filipuk,Alberto Lastra,Slawomir Michalik
Publisher : World Scientific
Page : 400 pages
File Size : 41,9 Mb
Release : 2022-03-03
Category : Mathematics
ISBN : 9781800611375

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Formal And Analytic Solutions Of Differential Equations by Galina Filipuk,Alberto Lastra,Slawomir Michalik Pdf

The book provides the reader with an overview of the actual state of research in ordinary and partial differential equations in the complex domain. Topics include summability and asymptotic study of both ordinary and partial differential equations, and also q-difference and differential-difference equations. This book will be of interest to researchers and students who wish to expand their knowledge of these fields.With the latest results and research developments and contributions from experts in their field, Formal and Analytic Solutions of Differential Equations provides a valuable contribution to methods, techniques, different mathematical tools, and study calculations.

Author : Jacques Sauloy
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 52,5 Mb
Release : 2016-12-07
Category : Galois theory
ISBN : 9781470430955

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Differential Galois Theory through Riemann-Hilbert Correspondence by Jacques Sauloy Pdf

Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equations, the main prerequisites are complex function theory, linear algebra, and an elementary knowledge of groups and of polynomials in many variables. A large variety of examples, exercises, and theoretical constructions, often via explicit computations, offers first-year graduate students an accessible entry into this exciting area.

Author : Michael Borinsky
Publisher : Springer
Page : 173 pages
File Size : 55,6 Mb
Release : 2018-11-04
Category : Science
ISBN : 9783030035419

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Graphs in Perturbation Theory by Michael Borinsky Pdf

This book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.

Author : Jean Zinn-Justin
Publisher : Oxford University Press, USA
Page : 544 pages
File Size : 49,6 Mb
Release : 2019-06-27
Category : Science
ISBN : 9780198787754

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From Random Walks to Random Matrices by Jean Zinn-Justin Pdf

Theoretical physics is a cornerstone of modern physics and provides a foundation for all modern quantitative science. It aims to describe all natural phenomena using mathematical theories and models, and in consequence develops our understanding of the fundamental nature of the universe. This books offers an overview of major areas covering the recent developments in modern theoretical physics. Each chapter introduces a new key topic and develops the discussion in a self-contained manner. At the same time the selected topics have common themes running throughout the book, which connect the independent discussions. The main themes are renormalization group, fixed points, universality, and continuum limit, which open and conclude the work. The development of modern theoretical physics has required important concepts and novel mathematical tools, examples discussed in the book include path and field integrals, the notion of effective quantum or statistical field theories, gauge theories, and the mathematical structure at the basis of the interactions in fundamental particle physics, including quantization problems and anomalies, stochastic dynamical equations, and summation of perturbative series.