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Asymptotic Behavior of Monodromy
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113 b
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1 837
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246
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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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