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Real and Complex Dynamical Systems Edited by Bodil Branner and Poul Hjorth Mathematical Institute, the Technical University of Denmark, Lyngby, Denmark Real and Complex Dynamical Systems edited by Bodil Branner and Poul Hjorth Mathematical Institute, The Technical University of Denmark, Lyngby, Denmark Springer-Science+Business Media, BV. NATO ASI Series Advanced Science Institutes Series A Series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The Series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Life Sciences Plenum Publishing Corporation B Physics London and New York C Mathematical and Physical Sciences Kluwer Academic Publishers D Behavioural and Social Sciences Dordrecht, Boston and London E Applied Sciences F Computer and Systems Sciences Springer·Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cell Biology Paris and Tokyo I Global Environmental Change PARTNERSHIP SUB·SERIES 1. Disarmament Technologies Kluwer Academic Publishers 2. Environment Springer-Verlag / Kluwer Academic Publishers 3. High Technology Kluwer Academic Publishers 4. Science and Technology Policy Kluwer Academic Publishers 5. Computer Networking Kluwer Academic Publishers The Partnership Sub-Series incorporates activities undertaken in collaboration with NA TO's Cooperation Partners, the countries of the CIS and Central and Eastern Europe, in Priority Areas of concern to those countries. NATO-PCO·DATA BASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords and/or abstracts) to more than 50000 contributions from international scientists published in all sections of the NATO ASI Series. Access to the NATO-PCO-DATA BASE is possible in two ways: - via online FILE 128 (NATO-PCG-DATA BASE) hosted by ESRIN, Via Galileo Galilei, 1-00044 Frascati, Italy. - via CD-ROM "NATO-PCG-DATA BASE" with user-friendly retrieval software in English, French and German (© WTV GmbH and DATAWARE Technologies Inc. 1989). The CD-ROM can be ordered through any member of the Board of Publishers or through NATO- PCO, Overijse, Belgium. Series C: Mathematical and Physical Sciences - Vol. 464 Proceedings of the NATO Advanced Study Institute on Real and Complex Dynamical Systems Hiller/IJd, Denmark June 2o-July 2, 1993 A C.I.P. Catalogue record for this book is available from the Library of Congress ISBN 978-90-481-4565-2 ISBN 978-94-015-8439-5 (eBook) DOI 10.1007/978-94-015-8439-5 AII Rights Reserved @ 1995 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1995 Softcover reprint of the hardcover 1st edition 1995 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, includ ing photo- copying, recording or by any information storage and retrieval system, without written permission from the copyright owner. TABLE OF CONTENTS Preface vii List of participants ix Viviane BALADI: Dynamical Zeta Functions 1 Chris BUDD: The Global Dynamics of Impact Oscillators ............... 27 Chris BUDD: Grazing in Impact Oscillators ..................... 47 Adrien DOUADY: Topological Entropy of Unimodal Maps .......... 65 John H. HUBBARD and Ralph W. OBERSTE-VORTH: H enon Mappings in the Complex Domain . 89 Bruce KITCHENS: Symbolic Dynamics, Group Automorphisms and Markov Partitions 133 Silvina P. DAWSON, Roza GALEEVA, John MILNOR and Charles TRESSER: A Monotonicity Conjecture for Real Cubic Maps 165 Colin SPARROW: Dynamics of Ordinary Differential Equations 185 Sebastian van STRIEN: Real Bounds in Complex Dynamics 211 Marcelo VIANA: Homoclinic Bifurcations and Strange Attractors 231 Jean-Christophe YOCCOZ: Introduction to Hyperbolic Dynamics 265 Lai-Sang YOUNG: Ergodic Theory of Differentiable Dynamical Systems 293 Index ................... 337 PREFACE This volume contains edited versions of 11 contributions given by main speakers at the NATO Advanced Study Institute on lReal and Complex Dynamical Systems in Hiller0d, Denmark, June 20th - July 2nd, 1993. The vision of the institute was to illustrate the interplay between two important fields of Mathematics: Real Dynamical Systems and Complex Dynamical Systems. The interaction between these two fields has been growing over the years. Problems in Real Dynamical Systems have recently been solved using complex tools in the real or by extension to the complex. In return, problems in Complex Dynamical Systems have been settled using results from Real Dynamical Systems. The programme of the institute was to examine the state of the art of central parts of both Real and Complex Dynamical Systems, to reinforce contact between the two aspects of the theory and to make recent progress in each accessible to a larger group of mathematicians. We wish to express our sincere thanks to all lecturers and participants for having helped to make this ASI a success. We acknowledge the extensive amount of time the invited main speakers had to spend to prepare the expository lectures, and to prepare their manuscripts for publication. Special thanks go to Adrien Douady, Se- bastian van Strien and Lai-Sang Young for their efforts as members of the Scientific Organizing Committee; moreover, to the conference secretaries Lone Aagesen and Tove Densted for their competent management of all matters great & small during the conference; to the very professional staff at the Apotekerforeningens Kursuse- jendom (where the Institute was held); and to two local participants, Pia Willumsen and Dan S0rensen for assistance above and beyond the call of mere participation. We would also like to thank Jacob Dylander and acknowledge his patient and carefull work of formatting and assembling the manuscripts of this book. The ASI was funded principally by NATO, with additional support from MIDIT (Modelling, Non-linear Dynamics and Irreversible Thermodynamics) at The Tech- nical University of Denmark, the Danish Natural Science Research Council, the Carlsberg Foundation, the Thomas B. Thrige Foundation, the Otto B. M0nsted Foundation, the Mathematical Institute at The Technical University of Denmark and the Danish Mathematical Society. We would like to thank all these organiza- tions for their support. For its efforts on behalf of this ASI we are most grateful to the Scientific Affairs Division of NATO, particularly to Dr. Luis V. da Cunha, the Director of the ASI programme. Bodil Branner, Scientific Director Poul Hjorth vii LIST OF PARTICIPANTS Simonette ABENDA Viviane BALADI S.I.S.S.A. Laboratoire de Mathematiques Via Beiruth, 4 Ecole Normale Superieure de Lyon 1-34014 Trieste 46, Allee d'Italie ITALY F -69364 Lyon Cedex 17 e-mail abenda<iltsmi19.sissa.it FRANCE and Raphael ALBRECHT Math. Department - ETH Ziirich Inst. fiir Theor. Physik, Lehrstuhl E ETH Zentrum Physikalische Inst. der RWTH Aachen Ramistrasse 101 Sommerfeldstrasse CH-S092 Ziirich D-52056 Aachen SWITZERLAND GERMANY e-mail baIadi<ilmath.ethz.eh e-mail raphael<il thphys.physik.rwth-aaehen.de Krzysztof BARANSKI Institute of Mathematics Ana Isabel ALONSO DE MENA Warsaw University E.T.S. Ingenieros Industriales ul. Banacha 2 Dept. Matematica AplicadaF a la In- PL-02-097 Warsaw genieria POLAND Paseo del Cauce In e-mail baranski<ilmimuw.edu.pl E-47011 Valladolid SPAIN Julia A. BARNES e-mail etmat3<i1epd.uva.es Math. Dept. CB # 3250 University of North Carolina at Chapel Jose FERREIRA ALVES Hill Faculdade de Ciencias Chapel Hill, NC 27599 Grupo de Matematica Pura UNITED STATES Praca Gomes Teixeira e-mail barnes <ilmath . une . edu P-4000 Porto PORTUGAL Bodil BRANNER e-mail jfaIves<ilfel.fe.up.pt Mathematical Institute The Technical University of Denmark Pau ATELA Building 303 Department of Mathematics DK-2S00 Lyngby Smith College DENMARK Northhampton, MA 01063 e-mail branner<ilmat.dtu.dk UNITED STATES e-mail pateIa<ilsophia.smith . edu ix x Jean-Yves BRIEND Amy CHIU Ecole Normale Superieure de Lyon Department of Mathematics 46, Allee d'Italie Boston University F -69364 Lyon Cedex 07 111, Cummington St. FRANCE Boston, MA 02215 e-mail ens-Iyon.:fr UNITED STATES e-mail olympiadIDmath. bu. edu Henk BRUIN Delft University of Technology Adrien DOUADY TWI General Mathematics Universite de Paris-Sud Mekelweg 4 Departement de Mathematiques NL-2600 GA Delft Batiment 425 NETHERLANDS F-91405 Orsay e-mail FRANCE e-mail adrien.douadylDens.fr Morten BR0NS Mathematical Institute Jakob DYLANDER The Technical University of Denmark Mathematical Institute Building 303 University of Copenhagen DK-2800 Lyngby Universitetsparken 5 DENMARK DK-2100 Copenhagen 0 e-mail bronsCOmat. dtu. elk DENMARK e-mail dylanderCOmath.ku.elk Chris BUDD School of Mathematics Adam EPSTEIN University of Bristol Department of Mathematics University Walk Cal. Tech. GB-Bristol, BS8 1TW Pasadena , CA UNITED KINGDOM UNITED STATES e-mail . uk e-mail elagolDcunyvm . bitnet Xavier BUFF Juan Francisco ESTRADA GARCIA Ecole Normale Superieure Universite de Paris-Sud 45 rue d'Ulm Departement de Mathematiques F-75005 Paris Cedex Batiment 425 FRANCE F-91405 Orsay Cedex e-mail bu:f:fIDens. ens.:fr FRANCE Manuel CHAVES Nuria FAGELLA Grupo de Matematica Pura Department of Mathematics Faculdade de Ciencias Boston University Praca Gomes Teixeira 111, Cummington St. P-4000 Porto Boston, MA 02215 PORTUGAL UNITED STATES e-mail machavesID:fc.up.pt e-mail nuria<Dmath. bu. edu xi FANG Jinqing Coby GEYSEL China Institute of Atomic Energy University of Amsterdam P.O. Box 275-27 Faculty of Math.F and Computer
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