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Author: B L J Braaksma
Publisher: World Scientific
ISBN: 9814487430
Category : Mathematics
Languages : en
Pages : 343
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Book Description
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: B L J Braaksma
Publisher: World Scientific
ISBN: 9814487430
Category : Mathematics
Languages : en
Pages : 343
Get Book Here
Book Description
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
ISBN: 9789812381729
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Offers a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations.
Author: B L J Braaksma
Publisher: World Scientific
ISBN: 9814548081
Category :
Languages : en
Pages : 342
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Book Description
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: B. L. J. BRAAKSMA
Publisher:
ISBN: 9789812776549
Category : Differential equations
Languages : en
Pages :
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Book Description
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 different.
Author: Boele Lieuwe Jan Braaksma
Publisher:
ISBN: 9789814531412
Category : Airy functions
Languages : en
Pages : 342
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Book Description
Author: Claude Sabbah
Publisher: Springer
ISBN: 9783642316944
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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: I︠U︡. S. Ilʹi︠a︡shenko
Publisher: American Mathematical Society(RI)
ISBN:
Category : Mathematics
Languages : en
Pages : 314
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Book Description
The nonlinear Stokes phenomenon occurs in the local theory of differential equations (or, more concisely, local dynamics) and finds application in singularity theory. This volume contains a number of papers on this subject, including a survey that begins with Stokes' pioneering works on linear theory and discusses the work of Voronin.
Author:
Publisher: Amer Mathematical Society
ISBN: 9780821841129
Category : Analytic space
Languages : en
Pages : 287
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Book Description
The nonlinear Stokes phenomenon occurs in the local theory of differential equations (or, more concisely, local dynamics) and finds application in singularity theory. This volume contains a number of papers on this subject, including a survey that begins with Stokes' pioneering works on linear theory and discusses the work of Voronin.
Author: Naofumi Honda
Publisher: Springer
ISBN: 4431557024
Category : Science
Languages : en
Pages : 133
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Book Description
The discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi–Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. As M.V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a remarkable paper in the Journal of Mathematical Physics indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary.
Author: Yasutaka Sibuya
Publisher: American Mathematical Soc.
ISBN: 0821846760
Category : Mathematics
Languages : en
Pages : 286
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Book Description
This book is a translation of a 1976 book originally written in Japanese. The main attention is paid to intrinsic aspects of problems related to linear ordinary differential equations in complex domains. Examples of the problems discussed in the book include the Riemann problem on the Riemann sphere, a characterization of regular singularities, and a classification of meromorphic differential equations. Since the original book was published, many new ideas have developed, such as applications of D-modules, Gevrey asymptotics, cohomological methods, $k$-summability, and studies of differential equations containing parameters. Five appendices, added in the present edition, briefly cover these new ideas. In addition, more than 100 references have been added. This book introduces the reader to the essential facts concerning the structure of solutions of linear differential equations in the complex domain and illuminates the intrinsic meaning of older results by means of more modern ideas. A useful reference for research mathematicians, this book would also be suitable as a textbook in a graduate course or seminar.
