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Lecture Notes in Mathematics

Asymptotic Behavior of Monodromy

Singularly Perturbed Differential Equations on a Riemann Surface

Authors: Simpson, Carlos

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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.

Table of contents (13 chapters)

  • Introduction

    Simpson, Carlos

    Pages 1-11

  • Ordinary differential equations on a Riemann surface

    Simpson, Carlos

    Pages 12-16

  • Laplace transform, asymptotic expansions, and the method of stationary phase

    Simpson, Carlos

    Pages 17-30

  • Construction of flows

    Simpson, Carlos

    Pages 31-40

  • Moving relative homology chains

    Simpson, Carlos

    Pages 41-53

Buy this book

eBook $29.99
price for USA in USD (gross)
  • ISBN 978-3-540-46641-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA in USD
  • ISBN 978-3-540-55009-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Asymptotic Behavior of Monodromy
Book Subtitle
Singularly Perturbed Differential Equations on a Riemann Surface
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1502
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-46641-3
DOI
10.1007/BFb0094551
Softcover ISBN
978-3-540-55009-9
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VI, 142
Topics