Asymptotic Behavior Of Monodromy
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Author |
: Carlos Simpson |
Publisher |
: Springer |
Total Pages |
: 154 |
Release |
: 1991 |
ISBN-10 |
: UOM:39015049318473 |
ISBN-13 |
: |
Rating |
: 4/5 (73 Downloads) |
Synopsis Asymptotic Behavior of Monodromy by : Carlos Simpson
This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.
Author |
: Carlos Simpson |
Publisher |
: |
Total Pages |
: 148 |
Release |
: 2014-01-15 |
ISBN-10 |
: 3662193620 |
ISBN-13 |
: 9783662193624 |
Rating |
: 4/5 (20 Downloads) |
Synopsis Asymptotic Behavior of Monodromy by : Carlos Simpson
Author |
: Elionora Arnold |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 500 |
Release |
: 2012-05-16 |
ISBN-10 |
: 9780817683436 |
ISBN-13 |
: 0817683437 |
Rating |
: 4/5 (36 Downloads) |
Synopsis Singularities of Differentiable Maps, Volume 2 by : Elionora Arnold
The present volume is the second in a two-volume set entitled Singularities of Differentiable Maps. While the first volume, subtitled Classification of Critical Points and originally published as Volume 82 in the Monographs in Mathematics series, contained the zoology of differentiable maps, that is, it was devoted to a description of what, where, and how singularities could be encountered, this second volume concentrates on elements of the anatomy and physiology of singularities of differentiable functions. The questions considered are about the structure of singularities and how they function.
Author |
: Lamberto Cesari |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 282 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642856716 |
ISBN-13 |
: 3642856713 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Asymptotic Behavior and Stability Problems in Ordinary Differential Equations by : Lamberto Cesari
In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call" qualitative theory of differential equations". The purpose of the present volume is to present many of the view points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.
Author |
: Elionora Arnold |
Publisher |
: Birkhäuser |
Total Pages |
: 492 |
Release |
: 2012-05-17 |
ISBN-10 |
: 0817683445 |
ISBN-13 |
: 9780817683443 |
Rating |
: 4/5 (45 Downloads) |
Synopsis Singularities of Differentiable Maps, Volume 2 by : Elionora Arnold
The present volume is the second in a two-volume set entitled Singularities of Differentiable Maps. While the first volume, subtitled Classification of Critical Points and originally published as Volume 82 in the Monographs in Mathematics series, contained the zoology of differentiable maps, that is, it was devoted to a description of what, where, and how singularities could be encountered, this second volume concentrates on elements of the anatomy and physiology of singularities of differentiable functions. The questions considered are about the structure of singularities and how they function.
Author |
: Sebastian Klein |
Publisher |
: Springer |
Total Pages |
: 326 |
Release |
: 2018-12-05 |
ISBN-10 |
: 9783030012762 |
ISBN-13 |
: 303001276X |
Rating |
: 4/5 (62 Downloads) |
Synopsis A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation by : Sebastian Klein
This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Euclidean 3-space. Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data. Finally, a Jacobi variety and Abel map for the spectral curve are constructed and used to describe the change of the spectral data under translation of the solution u. The book's primary audience will be research mathematicians interested in the theory of infinite-dimensional integrable systems, or in the geometry of constant mean curvature surfaces.
Author |
: Mark J. Ablowitz |
Publisher |
: Cambridge University Press |
Total Pages |
: 532 |
Release |
: 1991-12-12 |
ISBN-10 |
: 9780521387309 |
ISBN-13 |
: 0521387302 |
Rating |
: 4/5 (09 Downloads) |
Synopsis Solitons, Nonlinear Evolution Equations and Inverse Scattering by : Mark J. Ablowitz
This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
Author |
: Michel Marie Chipot |
Publisher |
: World Scientific |
Total Pages |
: 283 |
Release |
: 2024-04-15 |
ISBN-10 |
: 9789811290459 |
ISBN-13 |
: 9811290458 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Asymptotic Issues For Some Partial Differential Equations (Second Edition) by : Michel Marie Chipot
The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Author |
: R. B. White |
Publisher |
: World Scientific |
Total Pages |
: 430 |
Release |
: 2010 |
ISBN-10 |
: 9781848166080 |
ISBN-13 |
: 1848166087 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Asymptotic Analysis of Differential Equations by : R. B. White
"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Author |
: James Robert Buchanan |
Publisher |
: |
Total Pages |
: 226 |
Release |
: 1993 |
ISBN-10 |
: OCLC:29932880 |
ISBN-13 |
: |
Rating |
: 4/5 (80 Downloads) |
Synopsis Asymptotic Behavior of N-dimensional Systems of Ordinary Differential Equations of Kolmogorov-type by : James Robert Buchanan