Dynamics in Infinite Dimensions

Jack K. Hale, Luis T. Magalhaes, Waldyr Muniz Oliva

280 pages, parution le 28/08/2002 (2^eme édition)

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Résumé

This book presents an introduction to the geometric theory of infinite dimensional dynamical systems. Many of the fundamental results are presented for symptotically smooth dynamical systems that have applications to functional differential equations as well as classes of dissipative partial differential equations.
However, as in the earlier edition, the major emphasis is on retarded functional differential equations. This updated version also contains much material on neutral functional differential equations. The results in the earlier edition on Morse-Smale systems for maps are extended to a class of semiflows which include retarded functional differential equations and parabolic partial differential equations. Persistence of hyperbolicity under perturbations and nonuniform hyperbolicity also are discussed. There is a presentation of an interesting Morse decomposition of delay equations with negative feedback as well as a new chapter on a class on monotone dynamical systems for which transversality of stable and unstable manifolds always holds. Functional differential equations on a fixed finite dimensional space impose restrictions on the flow and may not include all ordinary differential equations. A complete discussion of these restrictions is given with a classification of those finite dimensional vector fields that can be realized on center manifolds. Included also is a complete theory of normal forms for retarded and neutral functional differential equations.
In addition to being useful for researchers in the field, the book is appropriate for a graduate course in dynamical systems.

Contents

Introduction
Invariant Sets and Attractors
Functional Differential Equations on Manifolds
The Dimension of the Attractor
Stability and Bifurcation
Stability of Morse-Smale Maps and Semiflows
One-to-oneness, Persistence and Hyperbolicity
Realization of Vector Fields and Normal Forms
Attractor Sets as C1-Manifolds
Monotonicity
The Kupka-Smale Theorem
Appendix A: Conley Index Theory in Noncompact Spaces
References
Index.

L'auteur - Jack K. Hale

Hale, J.K., Atlanta, GA, USA

L'auteur - Luis T. Magalhaes

Instituto Superior Tecnico, Lisbon, Portugal

L'auteur - Waldyr Muniz Oliva

Instituto Superior Tecnico, Lisbon, Portugal

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jack K. Hale, Luis T. Magalhaes, Waldyr Muniz Oliva
Parution	28/08/2002
Édition	2^eme édition
Nb. de pages	280
Format	16 x 24
Couverture	Relié
Poids	558g
Intérieur	Noir et Blanc
EAN13	9780387954639
ISBN13	978-0-387-95463-9