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

Dynamics in Infinite Dimensions

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Applied Mathematical Sciences 47
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-0-387-95463-9
• 2nd ed.
• Seitenzahl: 300
• Erscheinungstermin: 12. Juli 2002
• Englisch
• Abmessung: 241mm x 160mm x 21mm
• Gewicht: 552g
• ISBN-13: 9780387954639
• ISBN-10: 0387954635
• Artikelnr.: 10904726

Autorenporträt

Jack K. Hale, Georgia Tech, Atlanta, GA, USA / Luis Magalhaes, Instituto Superior Tecnico, Lisbon, Portugal / Waldyr Oliva, Instituto Superior Tecnico, Lisbon, Portugal

Inhaltsangabe

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.- A An Introduction to the Conley Index Theory in Noncompact Spaces.

Rezensionen

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 Polácik, Zentralblatt MATH, Vol. 1002 (2), 2003)