Invariant Manifolds
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583 M. W. Hirsch C. C. Pugh M. Shub
Invariant Manifolds
Springer-Verlag Berlin. Heidelberg • New York 1977
Authors
Morris W. Hirsch Charles C. Pugh Department of Mathematics, University of California Berkeley, CA 94720/USA
Michael Shub Department of Mathematics, Queens College City University of New York Flushing, NY 11367/USA
Library of Congress Cataloging in Publication Data
Hirsch~ Morris W 1933Invariant manifolds. (Lecture notes in mathematics ; 583) Bibliographsr: p. Includes index. 1. Riemannian manifolds. 2. Invaris~uts. 3- Sub~ manifolds. 4. Foliations (Mathematics) I. Pugh~ Charles C., 1940 joint author. II. Shub~ Michael~ 1942joint author. III. Title. IV. Series: Lecture notes in mathematics (Berlin) ; 583. QA3.L28 no. 583 [QA649] 510'.8s [514'.7] 77-5464
A M S Subject Classifications (1970): 3 4 C 3 0 , 3 4 C 4 0 , 3 4 C 3 5 , 58F10, 58F15, 5 7 D 3 0 , 5 7 D 5 0 , 5 7 E 2 0 ISBN 3-540-08148-8 ISBN 0-387-08148-8
Springer-Verlag Berlin • Heidelberg • N e w Y o r k Springer-Verlag N e w York • Heidelberg • Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks, Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Vertag Berlin - Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
INVARIANT MANIFOLDS M. Hirsch I ,
C. Pugh 2, M. Shub 3
Table o f Contents §I.
Introduction
. . . . . . . . . . . . . . . . . . . . . . . .
~2.
The L i n e a r Theory o f Normal H y p e r b o l i c i t y
. . . . . . . . .
5
§3.
The Cr S e c t i o n Theorem and L i p s c h i t z
. . . . . . . . .
25
~4.
The Local Theory o f Normally H y p e r b o l i c I n v a r i a n t Compact M a n i f o l d s . . . . . . . . . . . . . .
39
~5.
Pseudo H y p e r b o l i c i t y
53
Jets
and Plaque F a m i l i e s . . . . . . . . . .
1
~5A. Center M a n i f o l d s . . . . . . . . . . . . . . . . . . . . . .
64
~6.
. . . . . . . . . . . . . . .
67
. . . . . . . . . . . . . . .
108
Noncompactness and U n i f o r m i t y
~6A. Forced Smoothness o f i :
V ÷ H
~6B. Branched L a m i n a t i o n s . . . . . . . . . . . . . . . . . . . .
II0
~7,
115
Normally H y p e r b o l i c F o l i a t i o n s
and L a m i n a t i o n s . . . . . . .
~7A. Local Product S t r u c t u r e and Local S t a b i l i t y ~8.
. . . . . . . .
132
E q u i v a r i a n t F i b r a t i o n s and Nonwanderinq Sets . . . . . . . .
136
REFEREIICES . . . . . . . . . . . . . . . . . . . . . . . . .
145
Index
148
. . . . . . . . . . . . . . . . . . . . . . . . . . .
Ipartially
supported by N a t i o n a l Science Foundation Grant GP-29073.
2partially
supported by N a t i o n a l Science
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