Hamiltonian Mechanics: Integrability and Chaotic Behavior PDF
Preview Hamiltonian Mechanics: Integrability and Chaotic Behavior
Hamiltonian Mechanics Integrability and Chaotic Behavior 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 New York and London C Mathematical and Physical Sciences Kluwer Academic Publishers o Behavioral 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, Tokyo, Hong Kong, and Barcelona I Global Environmental Change Recent Volumes in this Series Volume 328 -Quantum Field Theory and String Theory edited by Laurent Baulieu, Vladimir Dotsenko, Vladimir Kazakov, and Paul Windey Volume 329 -Nonlinear Coherent Structures in Physics and Biology edited by K. H. Spatschek and F. G. Mertens Volume 330 -Coherent Optical Interactions in Semiconductors edited by R. T. Phillips Volume 331 -Hamiltonian Mechanics: Integrability and Chaotic Behavior edited by John Seimenis Volume 332 -Deterministic Chaos in General Relativity edited by David Hobill, Adrian Burd, and Alan Coley Volume 333 -Perspectives in the Structure of Hadronic Systems edited by M. N. Harakeh, J. H. Koch, and O. Scholten Volume 334 -Frontier Topics in Nuclear Physics edited by Werner Scheid and Aurel Sandulescu Volume 335 - Hot and Dense Nuclear Matter edited by Walter Greiner, Horst Stocker, and Andre Gallmann ~ Series B: Physics Hamiltonian Mechanics Integrability and Chaotic Behavior Edited by John Seimenis University of the Aegean Samos, Greece and N. Copernicus University Torun, Poland Springer Science+Business Media, LLC Proceedings of a NATO Advanced Research Workshop on Hamiltonian Mechanics, held June 28-July 2, 1993, in Torun, Poland NATO-PCO-DATA BASE The electronic index to the NATO ASI Series provides full bibliographical references (with keywords and/or abstracts) to more than 30,000 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-PCO-DATA BASE) hosted by ESRIN, Via Galileo Galilei, I-00044 Frascati, Italy —via CD-ROM "NATO Science and Technology Disk" with user-friendly retrieval software in English, French, and German (©WTV GmbH and DATAWARE Technologies, Inc. 1989). The CD-ROM also contains the AGARD Aerospace Database. The CD-ROM can be ordered through any member of the Board of Publishers or through NATO-PCO, Overijse, Belgium. Library of Congress Cataloging in Publication Information Hamiltonian mechanics : integrabi 1 ity and chaotic behavior / edited by John Seimenis. p. cm. — (MATO ASI series. Series B, Physics ; v. 331) xPublished in cooperation with NATO Scientific Affairs Division." "Proceedings of a NATO Advanced Research Workshop on Hamiltonian Mechanics, held June 28-Ju1 y 2, 1993, In Torun, Poland"—T.p. verso. Includes bibliographical references and index. ISBN 978-1-4899-0966-4 1. Mathematical physics—Congresses. 2. Hamiltonian systems- -Congresses. 3. Chaotic behavior in systems—Congresses. 4. Astrophysics—Mathematics—Congresses. I. Seimenis. John. II. North Atlantic Treaty Organization. Scientific Affairs Division. III. NATO Advanced Research Workshop on Hamiltonian Mechanics (1993 : Torun, Poland) IV. Series. QC19..H36 1994 530. 1 ' 55352~dc20 94-40008 CIP ISBN 978-1-4899-0966-4 ISBN 978-1-4899-0964-0 (eBook) DOI 10.1007/978-1-4899-0964-0 © Springer Science+Business Media New York 1994 Originally published by Plenum Press, New York in 1994 Softcover reprint of the hardcover 1st edition 1994 All rights reserved No part of this book 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 SPECIAL PROGRAM ON CHAOS, ORDER, AND PATTERNS This book contains the proceedings of a NATO Advanced Research Workshop held within the program of activities of the NATO Special Program on Chaos, Order, and Patterns. Volume 208 - MEASURES OF COMPLEXITY AND CHAOS edited by Neal B. Abraham, Alfonso M. Albano, Anthony Passamante, and Paul E. Rapp Volume 225 - NONLINEAR EVOLUTION OF SPATIO-TEMPORAL STRUCTURES IN DISSIPATIVE CONTINUOUS SYSTEMS edited by F. H. Busse and L. Kramer Volume 235 - DISORDER AND FRACTURE edited by J. C. Charmet, S. Roux, and E. Guyon Volume 236 - MICROSCOPIC SIMULATIONS OF COMPLEX FLOWS edited by Michel Mareschal Volume 240 - GLOBAL CLIMATE AND ECOSYSTEM CHANGE edited by Gordon J. MacDonald and Luigi Sertorio Volume 243 - DAVYDOV'S SOLITON REVISITED: Self-Trapping of Vibrational Energy in Protein edited by Peter L. Christiansen and Alwyn C. Scott Volume 244 - NONLINEAR WAVE PROCESSES IN EXCITABLE MEDIA edited by Arun V. Holden, Mario Markus, and Hans G. Othmer Volume 245 - DIFFERENTIAL GEOMETRIC METHODS IN THEORETICAL PHYSICS: Physics and Geometry edited by Ling-Lie Chau and Werner Nahm Volume 256 - INFORMATION DYNAMICS edited by Harald Atmanspacher and Herbert Scheingraber Volume 260 - SELF-ORGANIZATION, EMERGING PROPERTIES, AND LEARNING edited by Agnessa Babloyantz Volume 263 - BIOLOGICALLY INSPIRED PHYSICS edited by L. Peliti Volume 264 - MICROSCOPIC ASPECTS OF NONLINEARITY IN CONDENSED MADER edited by A. R. Bishop, V. L. Pokrovsky, and V. Tognetti Volume 268 - THE GLOBAL GEOMETRY OF TURBULENCE: Impact of Nonlinear Dynamics edited by Javier Jimenez SPECIAL PROGRAM ON CHAOS, ORDER, AND PATTERNS Volume 270 - COMPLEXITY, CHAOS, AND BIOLOGICAL EVOLUTION edited by Erik Mosekilde and Lis Mosekilde Volume 272 - PREDICTABILITY, STABILITY, AND CHAOS IN N-BODY DYNAMICAL SYSTEMS edited by Archie E. Roy Volume 276 - GROWTH AND FORM: Nonlinear Aspects edited by M. Ben Amar, P. Pelce, and P. Tabeling Volume 278 - PAINLEVE TRANSCENDENTS: Their Asymptotics and Physical Applications edited by Decio Levi and Pavel Winternitz Volume 280 - CHAOS, ORDER, AND PATTERNS edited by Roberto Artuso, Predrag Cvitanovic, and Giulio Casati Volume 284 - ASYMPTOTICS BEYOND ALL ORDERS edited by Harvey Segur, Saleh Tanveer, and Herbert Levine Volume 291 - PROTEIN TRANSFER IN HYDROGEN-BONDED SYSTEMS edited by T. Bountis Volume 292 - MICROSCOPIC SIMULATIONS OF COMPLEX HYDRODYNAMIC PHENOMENA edited by Michel Mareschal and Brad Lee Holian Volume 298 - CHAOTIC DYNAMICS: Theory and Practice edited by T. Bountis Volume 312 - FUTURE DIRECTIONS OF NONLINEAR DYNAMICS IN PHYSICAL AND BIOLOGICAL SYSTEMS edited by P. L. Christiansen, J. C. Eilbeck, and R. D. Parmentier Volume 320 - SINGULAR LIMITS OF DISPERSIVE WAVES edited by N. M. Ercolani, I. R. Gabitov, C. D. Levermore, and D. Serre Volume 323 - SOFT ORDER IN PHYSICAL SYSTEMS edited by Y. Rabin and R. Bruinsma Volume 329 - NONLINEAR COHERENT STRUCTURES IN PHYSICS AND BIOLOGY edited by K. H. Spatschek and F. G. Mertens Volume 331 - HAMILTONIAN MECHANICS: Integrability and Chaotic Behavior edited by John Seimenis PREFACE This volume contains invited papers and contributions delivered at the International Conference on Hamiltonian Mechanics: Integrability and Chaotic Behaviour, held in Tornn, Poland during the summer of 1993. The conference was supported by the NATO Scientific and Environmental Affairs Division as an Advanced Research Workshop. In fact, it was the first scientific conference in all Eastern Europe supported by NATO. The meeting was expected to establish contacts between East and West experts as well as to study the current state of the art in the area of Hamiltonian Mechanics and its applications. I am sure that the informal atmosphere of the city of Torun, the birthplace of Nicolaus Copernicus, stimulated many valuable scientific exchanges. The first idea for this cnference was carried out by Prof Andrzej J. Maciejewski and myself, more than two years ago, during his visit in Greece. It was planned for about forty well-known scientists from East and West. At that time participation of a scientist from Eastern Europe in an Organising Committee of a NATO Conference was not allowed. But always there is the first time. Our plans for such a "small" conference, as a first attempt in the new European situation -the Europe without borders - quickly passed away. The names of our invited speakers, authorities in their field, were a magnet for many colleagues from all over the world. More than one hundred and forty colleagues from twenty-five countries and all continents, expressed their interest to participate in our conference. Among them, distinguished scientists from the United States and the former Soviet Union. We were very glad to have the majority of them among us, in Tonm. The conference was funded by a major grant from NATO. Additional support was provided by the N. Copernicus University. I am indebted to Professor Andrzej Jamiolkowski, Rector of the N. Copernicus University and Chairman of the Local Organising Committee of our conference, for his continued help and support during the organisational period. I am sure that without his help, we would not have been able to finish this meeting succesfully. I would like to express my thanks to my colleague and friend Andrzej J. Maciejewski for his efforts during the time he was a member of the Scientific Organising Committee. Many thanks are due to Professors Carles Simo and Tassos Bountis for their advice as members of the Scientific Organising Committee. I would like to also thank, the members of the Local Organising Committee, Krzysztof Gozdziewski and Ewa Derkowska as well as the members of the staff of the Faculty of Physics and Astronomy of the N. Copernicus University for their help, during the period of the conference. All papers of the volume are refereed. I am indebted to the referees - especially to the external experts -for their kind assistance and their efforts to be fast, in order to give the volume for publication, in proper time. In the end, I would like to apologise to my son Kimon for the time I spent far from him, in order to finish successfully my work as Director of the NATO Advanced Research Workshop and editor of the proceedings. The part of the work that was carried out by me during the last two years, is dedicated to him. John Seimenis, Editor vii CONTENTS Invited papers Non-integrability criterion of Hamiltonian systems based on Ziglin's Theorem and its· relation to the singular point analysis ...................................................... .. H. Yoshida Averaging under fast quasiperiodic forcing . ..... ... .... ...... .............. .... ......... .... ...... 13 C. Simo Natural boundaries of normalizing transformations ........................................... 35 L. Billi, M. Malavasi and O. Turchetti Singular perturbation in Hamiltonian Mechanics .............. .................. .............. 43 A.D. Bruno The structure of Chaos ......................................................................................... 51 O. Contopouios From Integrability to Chaos: Examples of interrelations between physics and dynamics for minor bodies in the solar system .... .............. .......... ............... 73 C. Froeschle, Ph. Bendjoya and A. Cellino Successive elimination of harmonics: A way to explore the resonant structure of a Hamiltonian system ...................... .............. ........ .......... ................ 89 A. MorbideIli Periodic solutions of nonlinear Schrodinger equations and the Nash-Moser method ............................................................................................................... 103 W. Craig and C. Eugene Wayne On the tendency toward ergodicity with increasing number of degrees of freedom in Hamiltonian systems .. ....... ....... .......... .......... ............ ............... 123 L. Hurd, C. Grebogi and E.Ott Gibbsian check of the validity of Gibbsian calculation through dynamical observables ........ .... .............. .......... ....................... ................... ......... 131 D.F. Escande, H. Kantz, R. Livi and S. Ruffo Adiabatic invariants and time scales for energy sharing in models of classical gases ................................................................................................ 139 O. Benettin Numerical integration of Hamiltonian systems in the presence of additional integrals: Application of the observer method ................................. 153 A.J. Maciejewski and J-M Strelcyn viii Symmetries and topology of dynamical systems with two degrees of freedom .......................................................................................................... 167 V. Kozlov Contributed papers Variational criteria for nonintegrability and chaos in Hamiltonian systems .............................................................................................................. 173 S. Bolotin Exponentially small splitting in Hamiltonian systems ........ ...... .......... ...... ....... 181 A. Delshams and T.M. Seara Integrable and chaotic behaviour in the Paul trap and the hydrogen atom in a generalized van der Waals potential .......................................................... 189 D. Farrelly, I.E. Howard and T. Uzer Recent applications of Hamiltonian dynamics to accelerator physics ............. 197 E. Todesco Singularity analysis of 2D complexified Hamiltonian systems ....................... 205 S. Abenda and A. Bazzani Perturbation theory for systems without global action-angle coordinates .................................................. ..................................................... 213 F. Fasso A non-integrability test for perturbed Hamiltonian systems of two degrees of freedom ... ....................................................................................... 221 E. Meletlidou and S. Ichtiaroglou Librational invariant surfaces in the spin-orbit problem ................................ 229 A. Celletti Normalization of resonant Hamiltonians ......................................................... 237 D. Farrelly, I. Hwripherys and T. Uzer Effective stability for periodically perturbed Hamiltonian systems ." ............. 245 A. Jorba and C. Sima Bihamiltonian systems and Lax representation ............................................... 253 I.I. Morales and R. Ramirez An efficient method for computing periodic orbits of conservative dynamical systems ............................................................................................. 261 M.N. Vrahatis and T.C. Bountis The dynamics of trace maps ............................................................................. 275 I.A.G. Roberts and M. Baake Scars in groups of eigenfunctions .................................................................... 287 F. Borondo, G.G. de Polavieja and R.M. Benito A model of Poincare and rigorous proof of the second element of thermodynamics from mechanics ............................................................... 295 L.D. Pustyl'nikov Nekhoroshev and KAM theorems revisited via a unified approach ............... 299 A. Delshams and P. Gutierrez ix
The list of books you might like
