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  • Book
  • © 1991

Asymptotic Behavior of Monodromy

Singularly Perturbed Differential Equations on a Riemann Surface

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

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-IV
  2. Introduction

    • Carlos Simpson
    Pages 1-11
  3. Construction of flows

    • Carlos Simpson
    Pages 31-40
  4. Moving relative homology chains

    • Carlos Simpson
    Pages 41-53
  5. The main lemma

    • Carlos Simpson
    Pages 54-59
  6. Finiteness lemmas

    • Carlos Simpson
    Pages 60-67
  7. Sizes of cells

    • Carlos Simpson
    Pages 68-83
  8. Moving the cycle of integration

    • Carlos Simpson
    Pages 84-92
  9. Bounds on multiplicities

    • Carlos Simpson
    Pages 93-100
  10. Regularity of individual terms

    • Carlos Simpson
    Pages 101-110
  11. Complements and examples

    • Carlos Simpson
    Pages 111-126
  12. The Sturm-Liouville problem

    • Carlos Simpson
    Pages 127-134
  13. Back Matter

    Pages 135-139

About this book

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

  • Book Title: Asymptotic Behavior of Monodromy

  • Book Subtitle: Singularly Perturbed Differential Equations on a Riemann Surface

  • Authors: Carlos Simpson

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0094551

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-55009-9Published: 11 December 1991

  • eBook ISBN: 978-3-540-46641-3Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 142

  • Topics: Analysis, Algebraic Geometry

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions