Galois Theories Of Linear Difference Equations An Introduction

Author : Charlotte Hardouin,Jacques Sauloy,Michael F. Singer
Publisher : American Mathematical Soc.
Page : 171 pages
File Size : 48,9 Mb
Release : 2016-04-27
Category : Difference and functional equations -- Difference equations -- Linear equations
ISBN : 9781470426552

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Galois Theories of Linear Difference Equations: An Introduction by Charlotte Hardouin,Jacques Sauloy,Michael F. Singer Pdf

This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.

Author : Marius van der Put,Michael F. Singer
Publisher : Springer
Page : 182 pages
File Size : 54,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540692416

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Galois Theory of Difference Equations by Marius van der Put,Michael F. Singer Pdf

This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.

Author : Marius van der Put,Michael F. Singer
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642557507

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Galois Theory of Linear Differential Equations by Marius van der Put,Michael F. Singer Pdf

From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews

Author : Marius van der Put,Michael F. Singer
Publisher : Unknown
Page : 196 pages
File Size : 48,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662191776

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Galois Theory of Difference Equations by Marius van der Put,Michael F. Singer Pdf

Author : J. Chazarain,A. Piriou
Publisher : Elsevier
Page : 558 pages
File Size : 47,5 Mb
Release : 2011-08-18
Category : Computers
ISBN : 0080875351

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Introduction to the Theory of Linear Partial Differential Equations by J. Chazarain,A. Piriou Pdf

Introduction to the Theory of Linear Partial Differential Equations

Author : Jacques Sauloy
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 50,8 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 : Decio Levi,Raphaël Rebelo,Pavel Winternitz
Publisher : Springer
Page : 435 pages
File Size : 41,6 Mb
Release : 2017-06-30
Category : Science
ISBN : 9783319566665

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Symmetries and Integrability of Difference Equations by Decio Levi,Raphaël Rebelo,Pavel Winternitz Pdf

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.

Author : Lucia Di Vizio,Charlotte Hardouin
Publisher : American Mathematical Society
Page : 88 pages
File Size : 54,8 Mb
Release : 2022-08-31
Category : Mathematics
ISBN : 9781470453848

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Intrinsic Approach to Galois Theory of $q$-Difference Equations by Lucia Di Vizio,Charlotte Hardouin Pdf

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Author : Teresa Crespo,Zbigniew Hajto,Juan José Morales Ruiz
Publisher : Unknown
Page : 94 pages
File Size : 53,6 Mb
Release : 2007
Category : Electronic
ISBN : 8372424535

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Introduction to differential Galois theory by Teresa Crespo,Zbigniew Hajto,Juan José Morales Ruiz Pdf

Author : Bruno Anglès,Tuan Ngo Dac
Publisher : Springer Nature
Page : 337 pages
File Size : 46,8 Mb
Release : 2021-03-03
Category : Mathematics
ISBN : 9783030662493

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Arithmetic and Geometry over Local Fields by Bruno Anglès,Tuan Ngo Dac Pdf

This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.

Author : Walter G. Kelley,Allan C. Peterson
Publisher : Academic Press
Page : 403 pages
File Size : 44,7 Mb
Release : 2001
Category : Mathematics
ISBN : 012403330X

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Difference Equations by Walter G. Kelley,Allan C. Peterson Pdf

Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics. * Phase plane analysis for systems of two linear equations * Use of equations of variation to approximate solutions * Fundamental matrices and Floquet theory for periodic systems * LaSalle invariance theorem * Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory * Appendix on the use of Mathematica for analyzing difference equaitons * Exponential generating functions * Many new examples and exercises

Author : Alin Bostan,Kilian Raschel
Publisher : Springer Nature
Page : 544 pages
File Size : 41,9 Mb
Release : 2021-11-02
Category : Mathematics
ISBN : 9783030843045

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Transcendence in Algebra, Combinatorics, Geometry and Number Theory by Alin Bostan,Kilian Raschel Pdf

This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.

Author : Michio Kuga
Publisher : Unknown
Page : 168 pages
File Size : 48,7 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:49015002040401

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Galois' Dream by Michio Kuga Pdf

Author : Paul Mason Batchelder
Publisher : Unknown
Page : 230 pages
File Size : 53,9 Mb
Release : 1927
Category : Difference equations
ISBN : UCAL:B4249089

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An Introduction to Linear Difference Equations by Paul Mason Batchelder Pdf

Author : Johannes Blümlein,Carsten Schneider
Publisher : Springer Nature
Page : 551 pages
File Size : 47,8 Mb
Release : 2021-11-26
Category : Science
ISBN : 9783030802196

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Anti-Differentiation and the Calculation of Feynman Amplitudes by Johannes Blümlein,Carsten Schneider Pdf

This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.