Geometry and Dynamics of Integrable Systems
Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the
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Alexey Bolsinov Juan J. Morales-Ruiz Nguyen Tien Zung
Geometry and Dynamics of Integrable Systems
Advanced Courses in Mathematics CRM Barcelona Centre de Recerca Matemàtica Managing Editor: Enric Ventura
More information about this series at http://www.springer.com/series/5038
Alexey Bolsinov • Juan J. Morales-Ruiz Nguyen Tien Zung
Geometry and Dynamics of Integrable Systems Editors for this volume: Vladimir Matveev, Friedrich-Schiller-Universität Jena Eva Miranda, Universitat Politècnica de Catalunya
Alexey Bolsinov School of Mathematics Loughborough University Leicestershire, United Kingdom
Juan J. Morales-Ruiz Escuela Superior de Ingenieros de Caminos, Canales y Puertos Universidad Politécnica de Madrid Madrid, Spain
Nguyen Tien Zung Institut de Mathématiques Université Paul Sabatier Toulouse, France
ISSN 2297-0304 ISSN 2297-0312 (electronic) Advanced Courses in Mathematics - CRM Barcelona ISBN 978-3-319-33502-5 ISBN 978-3-319-33503-2 (eBook) DOI 10.1007/978-3-319-33503-2 Library of Congress Control Number: 2016957339 Mathematics Subject Classification (2010): 37J35, 37K10, 70H06, 12H05, 53D17 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser, www.birkhauser-science.com The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Foreword This book contains the elaborated version of lecture notes for the Advanced Course on Geometry and Dynamics of Integrable Systems which took place at the Centre de Recerca Matem`atica, CRM-Barcelona, in September 2013 during a CRM Special Research Program. Native to actual problem-solving problems in mechanics, the topic of Integrable Systems is currently on the crossroad of different disciplines in pure and applied mathematics and it has important interactions with physics. The study of integrable systems has had sp
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