Differential Equations And The Stokes Phenomenon
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| Author | : B L J Braaksma |
| Publisher | : World Scientific |
| Total Pages | : 343 |
| Release | : 2002-12-10 |
| Genre | : Mathematics |
| ISBN | : 9814487430 |
This volume is the record of a workshop on differential equations and the Stokes phenomenon, held in May 2001 at the University of Groningen. It contains expanded versions of most of the lectures given at the workshop. To a large extent, both the workshop and the book may be regarded as a sequel to a conference held in Groningen in 1995 which resulted in the book The Stokes Phenomenon and Hilbert's 16th Problem (B L J Braaksma, G K Immink and M van der Put, editors), also published by World Scientific (1996).Both books offer a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations. Apart from the asymptotics of solutions, Painlevé properties and the algebraic theory, new topics addressed in the second book include arithmetic theory of linear equations, and Galois theory and Lie symmetries of nonlinear differential equations.
| Author | : Boele Lieuwe Jan Braaksma |
| Publisher | : World Scientific |
| Total Pages | : 352 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9789812381729 |
Offers a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations.
| Author | : Claude Sabbah |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2012-10-04 |
| Genre | : Mathematics |
| ISBN | : 9783642316944 |
This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.
| Author | : B L J Braaksma |
| Publisher | : World Scientific |
| Total Pages | : 342 |
| Release | : 1996-05-06 |
| Genre | : |
| ISBN | : 9814548081 |
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.
| Author | : Boele Lieuwe Jan Braaksma |
| Publisher | : World Scientific Publishing Company Incorporated |
| Total Pages | : 327 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 9789810225674 |
| Author | : H.A. Antosiewicz |
| Publisher | : Academic Press |
| Total Pages | : 857 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483259137 |
International Conference on Differential Equations contains the proceedings of an International Conference on Differential Equations held at the University of Southern California, on September 3-7, 1974. The papers review advances in the qualitative-analytic theory of differential equations and highlight three broad areas: analytic theory (singular perturbations), qualitative theory (boundary value problems), and mathematical control theory (variational methods). Comprised of 82 chapters, this book begins with a discussion on continuous extensions, their construction, and their application in the theory of differential equations. The reader is then introduced to an approach to boundary control of partial differential equations based on the theory of semigroups of operators; lower closure and existence theorems in optimal control; and a nonlinear oscillation theorem. Subsequent chapters focus on matrices of rational functions; asymptotic integration of linear differential systems; solutions near bifurcated steady states; and geometric views in existence theory. This monograph will be of interest to students and instructors of mathematics.
| Author | : M. Kohno |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 539 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401146055 |
Since the initiative works for global analysis of linear differential equations by G.G. Stokes and B. Riemann in 1857, the Airy function and the Gauss hypergeometric function became the most important and the greatest practical special functions, which have a variety of applications to mathematical science, physics and engineering. The cffcctivity of these functions is essentially due to their "behavior in the large" . For instance, the Airy function plays a basic role in the asymptotic analysis of many functions arising as solutions of differential equations in several problems of applied math ematics. In case of the employment of its behavior, one should always pay attention to the Stokes phenomenon. On the other hand, as is well-known, the Gauss hypergeometric function arises in all fields of mathematics, e.g., in number theory, in the theory of groups and in analysis itself. It is not too much to say that all power series are special or extended cases of the hypergeometric series. For the full use of its properties, one needs connection formulas or contiguous relations.
| Author | : Philip Po-fang Hsieh |
| Publisher | : World Scientific |
| Total Pages | : 426 |
| Release | : 1994-04-08 |
| Genre | : |
| ISBN | : 9814552496 |
In this volume which honors Professors W A Harris, Jr, M Iwano, Y Sibuya, active researchers from around the world report on their latest research results. Topics include Analytic Theory of Linear and Nonlinear Differential Equations, Asymptotic Expansions, Turning Points Theory, Special Functions, Delay Equations, Boundary Value Problems, Sturm-Liouville Eigenvalues, Periodic Solutions, Numerical Solutions and other areas of Applied Mathematics.
| Author | : Marius van der Put |
| Publisher | : Springer |
| Total Pages | : 182 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354069241X |
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 | : Felipe Cano |
| Publisher | : Springer Nature |
| Total Pages | : 500 |
| Release | : |
| Genre | : |
| ISBN | : 3031541723 |
