Asymptotic Behavior of Monodromy [electronic resource] : Singularly Perturbed Differential Equations on a Riemann Surface / by Carlos Simpson.
Material type: TextSeries: Lecture Notes in Mathematics ; 1502Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1991Description: VI, 142 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540466413Subject(s): Mathematics | Geometry, algebraic | Global analysis (Mathematics) | Mathematics | Analysis | Algebraic GeometryAdditional physical formats: Printed edition:: No titleDDC classification: 515 LOC classification: QA299.6-433Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1431 |
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.
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.
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