Lyapunov Exponents Proceedings of a Conference held in Oberwolfach,
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Lecture Nates in Mathematics Editors: A. Dold, Heidelberg B. Eckmann, Zurich F. Takens, Groningen
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L. Arnold
H. Crauel I.-P. Eckmann (Eds.)
Lyapunov Exponents Proceedings of a Conference held in Oberwolfach, May 28 - June 2, 1990
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Editors Ludwig Arnold Institut fur Dynamische Systeme Universitat Bremen Postfach 330440 W-2800 Bremen 33, Germany Hans Crauel Fachbereich 9 Mathematik Universitat des Saarlandes W-6600 Saarbriicken II, Germany Jean-Pierre Eckmann Departement de Physique Theorique Universite de Geneve CH-12II Geneve 4, Switzerland Front cover: V. 1. Oseledets: A multiplicative ergodic theorem. Trudy Moskov. Mat. Obsc. 19 (1968),179-210
Mathematics Subject Classification (1980): Primary: 58F Secondary: 34F, 35R60, 58G32, 60F, 60G, 60H, 70L05, 70K, 73H, 13K, 93D, 93E
ISBN 3-540-54662-6 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-54662-6 Springer-Verlag New York Berlin Heidelberg 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, re-use of illustrations, 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 current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1991 Printed in Germany Typesetting: Camera ready by author Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 46/3140-543210 - Printed on acid-free paper
Preface These are the Proceedings of a conference on Lyapunov Exponents held at Oberwolfach May 28 June 2, 1990. The volume contains an introductory survey and 26 original research papers, some of which have, in addition, survey character. This conference was the second one on the subject of Lyapunov Exponents. The first one took place in Bremen in November 1984 and lead to the Proceedings volume Lecture Notes in Mathematics # 1186 (1986). Comparing those two volumes, one can realize pronounced shifts, particularly towards nonlinear and infinitedimensional systems and engineering applications. We would like to thank the 'Mathematisches Forschungsinstitut Oberwolfach' for letting us have the conference at this unique venue. March 1991
Ludwig Arnold (Bremen)
Hans Crauel (Saarbriicken)
JeanPierre Eckmann (Geneve)
Table of Contents Preface L. ARNOLD, H. CRAUEL Random Dynamical Systems
v 1
Chapter 1: Linear Random Dynamical Systems 1. YA. GOLDSHEID Lyapunov exponents and asymptotic behaviour of the product of random matrices
23
H. CRAUEL Lyapunov exponents of random dynamical systems' on Grassmannians
38
A. LEIZAROWITZ
Eigenvalue representation for the Lyapunov exponents of certain Markov processes
Y.
PERES
Analytic dependence of Lyapunov exponents on
