Dynamics in Infinite Dimensions

ISBN-13: 9781441930125 / Angielski / Miękka / 2010 / 282 str.

Jack K. Hale; Luis T. Magalhaes; Waldyr Oliva

Opis

State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications

Recenzje

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)

Spis treści

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: Conley Index Theory in Noncompact Spaces