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Asymptotic Behavior of Monodromy : Singularly Perturbed Differential Equations on a Riemann Surface - Carlos Simpson

Asymptotic Behavior of Monodromy

Singularly Perturbed Differential Equations on a Riemann Surface

Paperback

Published: 11th December 1991
Ships: 5 to 9 business days
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$57.13

This book concerns the question of how the solution of asystem of ODE's varies when the differential equationvaries. The goal is to give nonzero asymptotic expansionsfor the solution in terms of a parameter expressing how somecoefficients go to infinity. A particular classof familiesof equations is considered, where the answer exhibits a newkind of behavior not seen in most work known until now. Thetechniques include Laplace transform and the method ofstationary phase, and a combinatorial technique forestimating the contributions of terms in an infinite seriesexpansion for the solution. Addressed primarily toresearchers inalgebraic geometry, ordinary differentialequations and complex analysis, the book will also be ofinterest to applied mathematicians working on asymptotics ofsingular perturbations and numerical solution of ODE's.

Ordinary differential equations on a Riemann surface.- Laplace transform, asymptotic expansions, and the method of stationary phase.- Construction of flows.- Moving relative homology chains.- The main lemma.- Finiteness lemmas.- Sizes of cells.- Moving the cycle of integration.- Bounds on multiplicities.- Regularity of individual terms.- Complements and examples.- The Sturm-Liouville problem.

ISBN: 9783540550099
ISBN-10: 3540550097
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 142
Published: 11th December 1991
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 0.81
Weight (kg): 0.22