Dynamics in Infinite Dimensions

By: Jack K. Hale, Luis T. Magalhaes, Waldyr Oliva

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Hardcover | 12 July 2002 | Edition Number 2

At a Glance

Hardcover
296 Pages

Edition Type
Revised

Dimensions(cm)
24.13 x 15.88 x 1.91

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This book presents aspects of a geometric theory of infinite dimensional spaces with major emphasis on retarded functional differential equations. It contains results on Morse-Smale systems for semiflows, persistence of hyperbolicity under perturbations, nonuniform hyperbolicity, monotone dynamical systems, realization of vector fields on center manifolds and normal forms.

Industry Reviews

From the reviews of the second edition:

"This book presents a contemporary geometric theory of infinite-dimensional dynamical systems where the major emphasis is on retarded functional-differential equations. ... Each chapter contains some abstract theorems but the authors give some examples as well illustrating these general results and having interesting applications. ... This interesting book will be useful for researchers working in this field and, due to numerous examples, also for mathematicians working in applications." (Sergei A. Vakulenko, Mathematical Reviews, 2004 j)

"The first book, like the present one, is to a large extent devoted to functional differential equations. ... The present editions of chapters that appeared in the first book, Invariant sets and attractors, Functional differential equations on manifolds, The dimension of the attractor, Attractor sets as C¹-manifolds, The Kupka-Smale theorem, Conley index in noncompact spaces, are up-dated and contain additional examples. As the first book of the authors, the present one will be of interest and will be useful to a broad group of readers." (Peter Polacik, Zentralblatt MATH, Vol. 1002 (2), 2003)

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Preface
Introduction	p. 1
Invariant Sets and Attractors	p. 7
Functional Differential Equations on Manifolds	p. 19
The Dimension of the Attractor	p. 57
Stability and Bifurcation	p. 65
Stability of Morse-Smale Maps and Semiflows	p. 81
One-to-Oneness, Persistence, and Hyperbolicity	p. 109
Realization of Vector Fields and Normal Forms	p. 129
Attractor Sets as C[superscript 1]-Manifolds	p. 195
Monotonicity	p. 209
The Kupka-Smale Theorem	p. 229
Conley Index Theory in Noncompact Spaces	p. 241
References	p. 267
Index	p. 277
Table of Contents provided by Blackwell. All Rights Reserved.

Dynamics in Infinite Dimensions

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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