Global Theory of Dynamical Systems Proceedings of an International C

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819 Global Theory of Dynamical Systems Proceedings of an International Conference Held at Northwestern University, Evanston, Illinois, June 18-22, 1979

Edited by Z. Nitecki and C. Robinson

Springer-verlag Berlin Heidelberg New York 1980

Editors Zbigniew Nitecki Department of Mathematics, Tufts University Medford, MA 02155 USA Clark Robinson Department of Mathematics, Northwestern University Evanston, IL 60201 USA

AMS Subject Classifications (1980): 28 D xx, 34 C xx, 34 D xx, 54 H 20, 58 Fxx, 90Dxx ISBN 3-540-10236-1 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-10236-1 Springer-Verlag NewYork 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-Verlag Berlin Heidelberg 1980 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 214113140-543210

In Memoriam Rufus Bowen (February 23, 1947 - July 30, 1978) From his first paper on dynamical O. E. Lanford,

until his sudden,

systems,

was a leading figure in the development His earliest papers on topological underlying behavior.

systems

of dynamical

ful and comprehensive dynamic formalism"

character-

apsects of their stochastic he developed

theory of metric properties

and contributed

set the

relating geometric

to various

Together with Sinai and Ruelle,

axiom A systems,

systems theory.

entropy and subshifts

theme for much of his work,

istics of dynamical

written in 1968 with

tragic death in 1978, Rufus Bowen

of basic sets for

to the development

for the study of such systems.

the beauti-

of the "thermoBowen gave an

integrated exposition of this theory in his first book,

Equilibrium

States and the Ergodic Theory of Anosov Diffeomorphisms

(Springer

Lecture Notes in _Math. vol. 470, 1975).

His contributions

mical systems

the entropy conjecture,

touched diverse problems:

zeta functions, dynamics

maps of the interval,

chain-recurrence,

and ergodic theory for axiom A systems.

to dyna-

symbolic

Early in 1978,

working with C. Series, he began to study the ergodic theory of Fuchsian groups. (CBMS Regional

His second monograph,

Conference

concise but incisive theory in 1977. to be included de I'I.H.E.S.

introduction

spoken,

is a systems

of Bowen's prolific work is

in a dedicatory volume of the Publications

~thematiques

(volume 50, 1980).

in the late 1960's,

colleagues,

35, 1978)

to the state of dynamical

A complete bibliography

Those of us who knew Rufus, Berkeley

On Axiom A Diffeomorphisms

Series in Math., vol.

as (fellow)

graduate student at

and then as one of our most brilliant

remember a tall figure with a mass of red hair,

aler