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Asymptotic Behavior of Monodromy

Singularly Perturbed Differential Equations on a Riemann Surface

  • Book
  • © 1991

Overview

Authors:
  1. Carlos Simpson
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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
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  2. Introduction

    • Carlos Simpson
    Pages 1-11

  3. Ordinary differential equations on a Riemann surface

    • Carlos Simpson
    Pages 12-16

  4. Laplace transform, asymptotic expansions, and the method of stationary phase

    • Carlos Simpson
    Pages 17-30

  5. Construction of flows

    • Carlos Simpson
    Pages 31-40

  6. Moving relative homology chains

    • Carlos Simpson
    Pages 41-53

  7. The main lemma

    • Carlos Simpson
    Pages 54-59

  8. Finiteness lemmas

    • Carlos Simpson
    Pages 60-67

  9. Sizes of cells

    • Carlos Simpson
    Pages 68-83

  10. Moving the cycle of integration

    • Carlos Simpson
    Pages 84-92

  11. Bounds on multiplicities

    • Carlos Simpson
    Pages 93-100

  12. Regularity of individual terms

    • Carlos Simpson
    Pages 101-110

  13. Complements and examples

    • Carlos Simpson
    Pages 111-126

  14. The Sturm-Liouville problem

    • Carlos Simpson
    Pages 127-134

  15. Back Matter

    Pages 135-139
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Keywords

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.

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

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