Semidynamical Systems in Infinite Dimensional Spaces
Where do solutions go, and how do they behave en route? These are two of the major questions addressed by the qualita tive theory of differential equations. The purpose of this book is to answer these questions for certain classes of equa tions by recou
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Courant Institute of Mathematical Sciences
New York University New York, N.Y. 10012
Lawrence Sirovich
Division of Applied Mathematics
Brown University Providence, R.1. 02912
Joseph P. LaSalle
Division of Applied Mathematics
Lefschetz Center for Dynamical Systems Providence, R.1. 02912
ADVISORS H. Cabannes University of Paris-VI
J.K. Hale Brown University
J. Marsden Univ. of California at at Berkeley G.B. Whitham California Inst. of Technology
J. Keller Stanford University
EDITORIAL STATEMENT The mathematization of all sciences, the fading of traditional scientific boundaries, the impact of computer technology, the growing importance of mathematicalcomputer modelling and the necessity of scientific planning all create the need both in education and research for books that are introductory to and abreast of these developments. The purpose of this series is to provide such books, suitable for the user of mathematics, the mathematician interested in applications, and the student scientist. In particular, this series will provide an outlet for material less formally presented and more anticipatory of needs than finished texts or monographs, yet of immediate interest because of the novelty of its treatment of an application or of mathematics being applied or lying close to applications. The aim of the series is, through rapid publication in an attractive but inexpensive format, to make material of current interest widely accessible. This implies the absence of excessive generality and abstraction, and unrealistic idealization, but with quality of exposition as a goal. Many of the books will originate out of and will stimulate the development of new undergraduate and graduate courses in the applications of mathematics. Some of the books will present introductions· to new areas of research, new applications and act as signposts for new directions in the mathematical sciences. This series will often serve as an intermediate stage of the publication of material which, through exposure here, will be further developed and refined. These will appear in conventional format and in hard cover.
MANUSCRIPTS The Editors welcome all inquiries regarding the submission of. manuscripts for the series. Final preparation of all manuscripts will take place in the editorial offices of the series in the Division of Applied Mathematics, Brown University, Providence, Rhode Island. SPRINGER-VERLAG NEW YORK INC., 175 Fifth Avenue, New York, N. Y. 10010
Applied Mathematical Sciences I Volume 37
Stephen H. Saperstone
Semidynamical Systems in Infinite Dimensional Spaces
Springer-Verlag New York Heidelberg
Berlin
Stephen H. Saperstone George Mason University Department of Mathematics 4400 University Drive Fairfax, V A 22030 U.S.A.
Library of Congress Cataloging in Publication Data Saperstone, Stephen H. Semidynamical systems in infinite dimensional spaces. (Applied mathematical sciences; v. 37) Bibliography: p. Includes indexes. 1. Differentiable dynamical systems. 2. Topological imbeddings. 3. Function spaces. I. Title. II. Se
