The Riemann Hilbert Problem
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The Riemann Hilbert Problem
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Author : D. V. Anosov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
The Riemann Hilbert Problem written by D. V. Anosov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book is devoted to Hilbert's 21st problem (the Riemann-Hilbert problem) which belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concems the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this tumed out to be a rare case of a wrong forecast made by hirn. In 1989 the second author (A.B.) discovered a counterexample, thus 1 obtaining a negative solution to Hilbert's 21st problem. After we recognized that some "data" (singularities and monodromy) can be obtai ned from a Fuchsian system and some others cannot, we are enforced to change our point of view. To make the terminology more precise, we shaII caII the foIIowing problem the Riemann-Hilbert problem for such and such data: does there exist a Fuchsian system having these singularities and monodromy? The contemporary version of the 21 st Hilbert problem is to find conditions implying a positive or negative solution to the Riemann-Hilbert problem.
The Riemann Hilbert Problem
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Author : D. V. Anosov
language : en
Publisher:
Release Date : 1994
The Riemann Hilbert Problem written by D. V. Anosov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Aspects Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1981
Aspects Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.
Riemann Hilbert Problems Their Numerical Solution And The Computation Of Nonlinear Special Functions
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Author : Thomas Trogdon
language : en
Publisher: SIAM
Release Date : 2015-12-22
Riemann Hilbert Problems Their Numerical Solution And The Computation Of Nonlinear Special Functions written by Thomas Trogdon and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-22 with Mathematics categories.
Riemann?Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann?Hilbert problem.This book, the most comprehensive one to date on the applied and computational theory of Riemann?Hilbert problems, includes an introduction to computational complex analysis, an introduction to the applied theory of Riemann?Hilbert problems from an analytical and numerical perspective, and a discussion of applications to integrable systems, differential equations, and special function theory. It also includes six fundamental examples and five more sophisticated examples of the analytical and numerical Riemann?Hilbert method, each of mathematical or physical significance or both.?
Recent Developments In Integrable Systems And Riemann Hilbert Problems
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Author : Kenneth T-R McLaughlin
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Recent Developments In Integrable Systems And Riemann Hilbert Problems written by Kenneth T-R McLaughlin 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 2003 with Mathematics categories.
This volume is a collection of papers presented at a special session on integrable systems and Riemann-Hilbert problems. The goal of the meeting was to foster new research by bringing together experts from different areas. Their contributions to the volume provide a useful portrait of the breadth and depth of integrable systems. Topics covered include discrete Painleve equations, integrable nonlinear partial differential equations, random matrix theory, Bose-Einstein condensation, spectral and inverse spectral theory, and last passage percolation models. In most of these articles, the Riemann-Hilbert problem approach plays a central role, which is powerful both analytically and algebraically. The book is intended for graduate students and researchers interested in integrable systems and its applications.
Linear Differential Equations And Group Theory From Riemann To Poincare
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Author : Jeremy Gray
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-21
Linear Differential Equations And Group Theory From Riemann To Poincare written by Jeremy Gray and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-21 with Mathematics categories.
This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
Deformation Of Connections The Riemann Hilbert Problem And Tau Functions
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Author : Gerard Helminck
language : nl
Publisher:
Release Date : 1986
Deformation Of Connections The Riemann Hilbert Problem And Tau Functions written by Gerard Helminck and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
The 21st Hilbert Problem For Linear Fuchsian Systems
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Author : A. A. Bolibrukh
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
The 21st Hilbert Problem For Linear Fuchsian Systems written by A. A. Bolibrukh 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 1995 with Mathematics categories.
Bolibrukh presents the negative solution of Hilbert's twenty-first problem for linear Fuchsian systems of differential equations. Methods developed by Bolibrukh in solving this problem are then applied to the study of scalar Fuchsian equations and systems with regular singular points on the Riemmann sphere.
The Stokes Phenomenon And Hilbert S 16th Problem
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Author : B L J Braaksma
language : en
Publisher: World Scientific
Release Date : 1996-05-06
The Stokes Phenomenon And Hilbert S 16th Problem written by B L J Braaksma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-06 with categories.
The 16th Problem of Hilbert is one of the most famous remaining unsolved problems of mathematics. It concerns whether a polynomial vector field on the plane has a finite number of limit cycles. There is a strong connection with divergent solutions of differential equations, where a central role is played by the Stokes Phenomenon, the change in asymptotic behaviour of the solutions in different sectors of the complex plane.The contributions to these proceedings survey both of these themes, including historical and modern theoretical points of view. Topics covered include the Riemann-Hilbert problem, Painleve equations, nonlinear Stokes phenomena, and the inverse Galois problem.