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ADVENTURES IN ORDER AND CHAOS ASTROPHYSICS AND SPACE SCIENCE LIBRARY VOLUME 313 EDITORIAL BOARD Chairman W.B. BURTON, National Radio Astronomy Observatory, Charlottesville, Virginia, U.S.A. ([email protected]); University of Leiden, The Netherlands ([email protected]) Executive Committee J. M. E. KUIJPERS, Faculty of Science, Nijmegen, The Netherlands E. P. J. VAN DEN HEUVEL, Astronomical Institute, University of Amsterdam, The Netherlands H. VAN DER LAAN, Astronomical Institute, University of Utrecht, The Netherlands MEMBERS I. APPENZELLER, Landessternwarte Heidelberg-Königstuhl, Germany J. N. BAHCALL, The Institute for Advanced Study, Princeton, U.S.A. F. BERTOLA, Universitá di Padova, Italy J. P. CASSINELLI, University of Wisconsin, Madison, U.S.A. C. J. CESARSKY, Centre d'Etudes de Saclay, Gif-sur-Yvette Cedex, France O. ENGVOLD, Institute of Theoretical Astrophysics, University of Oslo, Norway R. McCRAY, University of Colorado, JILA, Boulder, U.S.A. P. G. MURDIN, Institute of Astronomy, Cambridge, U.K. F. PACINI, Istituto Astronomia Arcetri, Firenze, Italy V. RADHAKRISHNAN, Raman Research Institute, Bangalore, India K. SATO, School of Science, The University of Tokyo, Japan F. H. SHU, University of California, Berkeley, U.S.A. B. V. SOMOV, Astronomical Institute, Moscow State University, Russia R. A. SUNYAEV, Space Research Institute, Moscow, Russia Y. TANAKA, Institute of Space & Astronautical Science, Kanagawa, Japan S. TREMAINE, CITA, Princeton University, U.S.A. N. O. WEISS, University of Cambridge, U.K. ADVENTURES IN ORDER AND CHAOS A Scientific Autobiography By GEORGE CONTOPOULOS Member of the Academy of Athens, Research Centre of Astronomy, Athens, Greece KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 1-4020-3039-8 (HB) ISBN 1-4020-3040-1 (e-book) Published by Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and South America by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers, P.O. Box 322, 3300 AH Dordrecht, The Netherlands. Printed on acid-free paper springeronline.com All Rights Reserved © 2004 Kluwer Academic Publishers No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands. Contents Preface ix 1 YEARS OF STUDY 1 2 THESIS 4 3 FIRST TRIPS ABROAD 7 4 APPOINTMENT AS A PROFESSOR 9 5 THE THIRD INTEGRAL 13 6 TO THE UNITED STATES (THROUGH MOSCOW) 17 7YALE 18 8 CHANDRASEKHAR 24 9 PRINCETON - NEW YORK 28 10 FIRST IAU SYMPOSIUM IN DYNAMICAL ASTRONOMY 32 11 IAU COMMISSION 33 35 12 APPLICATIONS OF THE THIRD INTEGRAL 37 12.1 Celestial Mechanics 37 12.2 Galactic Dynamics 38 12.3 The Fermi-Pasta-Ulam Problem 39 12.4 The Stormer¨ Problem 39 12.5 Solitons 40 12.6 Other Applications 40 12.7 The Breakdown of the Third Integral 41 13 RESONANCE OVERLAP 41 14 THE JUNTA PERIOD AND THE IAU 44 15 SECOND SABBATICALIN THE USA. THE DENSITY WAVE THEORY 49 16 A VISIT TO ISRAEL 55 vi ADVENTURES IN ORDER AND CHAOS 17 FIRST IAU REGIONAL MEETING 56 18 CONTACTS IN ITALY 59 19 SERVICE IN THE IAU 61 20 IAU SECRETARIAT 67 21 VISITS TO THE USSR 69 22 TOPOLOGICAL METHODS IN GALACTIC DYNAMICS 76 23 THE IAU GENERAL ASSEMBLY IN GRENOBLE 80 24 A SABBATICAL AT ESO 82 25 ASTRONOMY AND ASTROPHYSICS 85 26 TRAVELLING IN WESTERN EUROPE 89 27 DESTRUCTION OF THE INTEGRALS 91 28 SYSTEMS OF THREE DEGREES OF FREEDOM 93 29 BIFURCATIONS 98 30 THE IAU GENERAL ASSEMBLY IN GREECE 100 31 BROUWER PRIZE 103 32 VISITS TO ESO 105 33 TERMINATION OF SPIRALS AND BARS 107 34 FURTHER TRAVEL 108 35 ORDER AND CHAOS 113 36 RELATIVITY AND COSMOLOGY 117 37 QUANTUM MECHANICS VS CLASSICAL MECHANICS 124 38 UNIVERSITY OF FLORIDA 126 39 INTEGRABLE MODELS 131 40 ESCAPES 132 41 POTENTIALS WITHOUT ESCAPES 134 42 CHAOS AND RANDOMNESS 135 43 HOMOCLINIC AND HETEROCLINIC TANGLES 139 44 HONORARY DEGREE FROM THE UNIVERSITY OF CHICAGO 142 45 DYNAMICAL SPECTRA 143 46 DESTRUCTION OF ISLANDS OF STABILITY 145 47 STICKINESS 148 48 COLLABORATORS IN GREECE 150 49 COLLABORATORS ABROAD 152 Contents vii 50 OUR FACULTY 154 51 NATO 157 52 MOTIVATION 163 53 PAPERS AND REFEREES 168 54 LECTURES 174 55 ACADEMY OF ATHENS 176 56 PROSPECTS FOR THE FUTURE 181 References 185 Preface For many years I was organizing a weekly seminar on dynamical astronomy, and I used to make some historical remarks on every subject, including some anecdotes from my contacts with many leading scientists over the years. I described also the development of various subjects and the emergence of new ideas in dynamical astronomy. Then several people prompted me to write down these remarks, which cannot be found in papers, or books. Thus, I decided to write this book, which contains my experiences over the years. I hope that this book may be helpful to astronomy students all over the world. During my many years of teaching, as a visiting professor, in American Universities (1962-1994, Yale, Harvard, MIT, Cornell, Chicago, Maryland and Florida) I was impressed by the quality of my graduate students. Most of them were very bright, asking penetrating questions, and preparing their homework in a perfect way. In a few cases, instead of a final examination, I assigned to them some small research projects and they presented their results at the end of the course. They were excellent in preparing the appropriate slides and in presenting their results in a concise and clear way. On the other hand my Greek students, and students of several European Uni- versities, were shy, awkward with the English language, and had difficulties presenting their work. But all this changed in the last twenty years. At a doc- toral school in Thessaloniki during 1993 (Contopoulos et al. 1994b) about 50 students from many European countries were asked to make short presentations of their doctoral research. This time their presentations were perfect. They had nothing to envy from their American colleagues. The change was not easy. It required a major effort to overcome the diffi- culties of the language, to learn how to find and use the literature, and how to present their results in a clear way. I remember an assistant of mine, who had difficulty in speaking English in our seminars (we used English for practice). But I insisted. And the outcome x ADVENTURES IN ORDER AND CHAOS was that a few years later he was a professor, and an associate editor of an international journal of Astronomy. Thus, I want to encourage students to try hard. Even if they come from a remote country, or region, they can excell in international science. My scientific autobiography relates my own efforts to overcome the diffi- culties of my background and reach the most up-to-day problems of dynamical astronomy. In particular it describes how I became involved in many prob- lems, from celestial mechanics to cosmology, and what were the main ideas that guided me over the years. Finally I describe my experience in writing and refereeing papers, and in preparing lectures, as well as my thoughts about the future of dynamical astronomy and of related fields. 1 1. YEARS OF STUDY I was born in a relatively small Greek town on the northern coast of Pelo- ponnese, called Aigion. I attended primary and secondary school there. At the same time I started studying French, German and English. My mother was a teacher of mathematics at a high school (she was the first Greek girl to study mathematics). My father was a lawyer. But he had a broader education, and he was fond of reading popular books on science, especially in French. I remember that when I was 10 years old he tried to teach me relativity theory. Maybe I did not learn much at that time but I was impressed by the theories of physics and I started wanting to explore the Universe. During my high school years our country was occupied by foreign troops. Greece had conducted a victorious campaign when it was attacked by the Ital- ian dictator Mussolini in 1940. The invaders were defeated and Greek troops entered deeply into Albania during 1940-1941. But then Hitler came to rescue his partner. The armoured German forces attacked Greece from its back, the weakly protected border with Bulgaria. Thus, Greece was defeated and was occupied by German troops for about four years. During most of that time Italian and Bulgarian troops participated in the occupation forces. School continued, but with many difficulties. Our Gymnasium, one of the best buildings of our town, was taken by the occupation forces. Classes were continued in churches and in private houses. An immediate consequence of the occupation was starvation. Many people died of hunger, especially in Athens. The salary of my mother practically vanished because of the enormous inflation (after the occupation one new drachma was set equivalent to 50 billion infla- tionary drachmas). And my father had to take care of six children and three elderly grandparents. We survived only because we were lucky enough to own a small farm outside the town. This farm contained many fruit trees, orange, apple, cherry and olive trees. We cultivated the soil under the trees twice a year, first with corn, and then with maize and vegetables.

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