Ergodic Theory and Differentiable Dynamics
This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a
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Editorial Board
E. Bombieri, Princeton S. Feferman, Stanford N. H. Kuiper, Bures-sur-Yvette P. Lax, New York R. Remmert (Managing Editor), Munster W. Schmid, Cambridge, Mass. J-P. Serre, Paris J. Tits, Paris
Ricardo Mane
Ergodic Theory and Differentiable Dynamics Translated from the Portuguese by Silvio Levy With 32 Figures
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Ricardo Mane I. M. P.A. Estrada Dona Castorina 110 22460 Rio de Janeiro RJ Brasil Silvio Levy Dept. of Mathematics Princeton University Princeton, New Jersey, 08544 U.S.A.
Title of the original Portuguese edition: Introduc;ao a Teoria Erg6dica ..(0 1983 by Ricardo Mane
Mathematics Subject Classification (1980): 58 F 11, 58 Fl5
ISBN-13 :978-3-642-70337-9 e-ISBN-13 :978-3-642-70335-5 DOl: 10.1007/978-3-642-70335-5 Library of Congress Cataloging-in-Publication Data ~afte,Ricardo, 1948Ergodic theory and differentiable dynamics (Ergebnisse der Mathematik und ihrer Grenzgebiete; 3. Folge, Bd. 8) Translation of: Introdu9ao it teoria erg6dica. Bibliography: p. Includes index. I. Ergodic theory. 2. ~easure theory. I. Title. II. Series. QA614.~3613 1987 515.4'2 86-25983 ISBN-13 :978-3-642-70337-9 (U.S.) This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9,1965, in its version of June 24,1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. 1) Springer-Verlag Berlin Heidelberg 1987 Softcover reprint of the hardcover 1st edition 1987
Typesetting: Asco Trade Typesetting Ltd., Hong Kong 2141/3140-543210
To A lexandre, Claus, Paulinho and Zeze
Preface to the English Edition
This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in contemporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the corrections mentioned above. Rio de Janeiro, January 1987
Ricardo Mane
Introduction
This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentia
