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Asymptotic Behavior of Monodromy

Singularly Perturbed Differential Equations on a Riemann Surface

  • Authors
  • CarlosĀ Simpson

Part of the Lecture Notes in Mathematics book series (LNM, volume 1502)

Table of contents

  1. Front Matter
    Pages I-IV
  2. Carlos Simpson
    Pages 1-11
  3. Carlos Simpson
    Pages 31-40
  4. Carlos Simpson
    Pages 41-53
  5. Carlos Simpson
    Pages 54-59
  6. Carlos Simpson
    Pages 60-67
  7. Carlos Simpson
    Pages 68-83
  8. Carlos Simpson
    Pages 84-92
  9. Carlos Simpson
    Pages 93-100
  10. Carlos Simpson
    Pages 101-110
  11. Carlos Simpson
    Pages 111-126
  12. Carlos Simpson
    Pages 127-134
  13. Back Matter
    Pages 135-139

About this book

Introduction

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.

Keywords

Asymptotic methods for ODE Ordinary differential equations differential equation monodromy Laplace transform ordinary differential equation singular perturbation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0094551
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-55009-9
  • Online ISBN 978-3-540-46641-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site