Proximal Flows
- PDF / 6,430,796 Bytes
- 161 Pages / 461 x 684 pts Page_size
- 71 Downloads / 285 Views
517
Shmuel Glasner
Proximal Flows ETHICS ETH-BIB
IIIIIIIIIiIIllll 00100000802833
Springer-Verlag Berlin. Heidelberg- NewYork 1976
Author Shmuel Glasner Department of Mathematical Sciences TeI-Aviv University TeI-Aviv/Israel
Ubrary of Congress Cataloging in PublleaUon Data
Glasner, Shmuel, 1945Proximal flows. (Lecture notes in mathematics ; 517) "An elaboration on notes taken ... ~ a course entitled 'Topics in topical dynam/cs,' which was given by the author in the spring semester of the academic year 1973-74 at the thuiversity of Maryland." Bibliography: p. i. Topological dynasties. 2. Lie groups. 3. Harmonic functicms. I. Title. IX. Series : Lecture notes in mathematics (Ber]-in) ; 517, QA3.L28 no. 517 [QA611.5] 510'.8s [51~'.7] 76-9866
AMS Subject Classifications (1970): 43A85, 54H15, 54H20, 54H25, 57E20, 60B05 ISBN 3-540-07689-1 ISBN 0-387-07689-1
Springer-Verlag Berlin Heidelberg 9 N 9 ewYork Springer-Verlag New York Heidelberg 9 Berlin 9
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 w 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. 9by Springer-Verlag Berlin 9Heidelberg 1976 Printed in Germany Printing and binding: Beltz Offsetdruck, HemsbachlBergstr.
TO RUTH
PREFACE This work is an elaboration on notes taken, N. Markley,
during a course entitled
mainly by Professor
"Topics in topological dynamicW'
which was given by the author in the spring semester of the academic year 1973-74 at the University of Maryland.
The main theme on which
these notes are based is the notion of proximality. exploited in two principal directions.
The first one is the abstract
"algebraic" theory of topological dynamics, the other is
This notion is
created by R. Ellis,
and
H. Furstenberg's theory of boundaries for Lie groups and
of harmonic functions.
Admittedly these two theories have different
flavors and use different techniques,
yet we think that an interaction
between ~hem might be fruitful. A good example of this interaction is Furstenberg's characterization of continuous harmonic functions on a symmetric space as those continuous functions in weak
,
topology)
s
whose orbit closure
is a strongly proximal flow,
D = G/~ (in the
(Theorem VI.3.1.).
Other instances are the concrete identification of the universal stmongly proximal flow and the generalized strong Bohr compactification of a connected semisimple Lie group with a finite center, and VIII.3.6.
(Theorems IV.3.2.
respectively).
The notes are divided into ten chapters each starting.with a short introduction~
which describes the material included and indi-
cates its main sources.
The prerequisites
for reading the "pure"
topological dynamics parts are just
Data Loading...
