Asymptotic behavior of monodromy
Subtitle: singularly perturbed differential equations on a Riemann surface
By: Carlos Simpson.
Series: Lecture notes in mathematics ;; 1502; Lecture notes in mathematics (Springer-Verlag) ;; 1502.
Publisher: Springer-Verlag
Published: 1991
Place of publication: Berlin; New York
Language: eng
Number of pages: 139
Subjects: Differential equations -- Asymptotic theory; Riemann surfaces
Description: 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.
Notes: Includes bibliographical references (p. [135]-137) and index.