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Delay Equations : Functional-, Complex-, and Nonlinear Analysis - O. Diekmann

Delay Equations

Functional-, Complex-, and Nonlinear Analysis

Hardcover Published: 9th May 1995
ISBN: 9780387944166
Number Of Pages: 536

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The aim of this book is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple, yet rich, class of examples, that is, those described by delay differential equations. It is a textbook giving detailed proofs and providing many exercises, which is intended both for self-study and for courses at a graduate level. The book would also be suitable as a reference for basic results. As the subtitle indicates, the book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. After studying this book, the reader should have a working knowledge of applied functional analysis and dynamical systems.

Introduction and previewp. 1
Linear autonomous RFDEp. 11
The shift semigroupp. 36
Linear RFDE as bounded perturbationsp. 51
Spectral theoryp. 95
Completeness or small solutions?p. 135
Inhomogeneous linear systemsp. 193
Semiflows for nonlinear systemsp. 201
Behaviour near a hyperbolic equilibriump. 242
The center manifoldp. 259
Hopf bifurcationp. 287
Characteristic equationsp. 302
Time-dependent linear systemsp. 339
Floquet Theoryp. 355
Periodic orbitsp. 364
The prototype equation for delayed negative feedback: periodic solutionsp. 379
On the global dynamics of nonlinear autonomous differential delay equationsp. 426
App. I Bounded variation, measure and integrationp. 443
App. II Introduction to the theory of strongly continuous semigroups of bounded linear operators and their adjointsp. 452
App. III The operational calculusp. 474
App. IV Smoothness of the substitution operatorp. 482
App. V Tangent vectors, Banach manifolds and transversalityp. 492
App. VI Fixed points of parameterized contractionsp. 497
App. VII Linear age-dependent population growth: elaboration of some of the exercisesp. 500
App. VIII The Hopf bifurcation theoremp. 505
Referencesp. 514
Indexp. 530
List of symbolsp. 533
List of notationp. 533
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387944166
ISBN-10: 0387944168
Series: Applied Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 536
Published: 9th May 1995
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.4 x 15.6  x 3.81
Weight (kg): 2.09

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