Vladimir I. Arnold - Collected Works Hydrodynamics, Bifurcation Theo
Vladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collecte
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Collected Works volume ii Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965–1972
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VLADIMIR I. ARNOLD
Collected Works
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Vladimir I. Arnold, drawing, 1968. Photo by Dmitry Arnold
VLADIMIR I. ARNOLD Collected Works
VLADIMIR I. ARNOLD
Collected Works
VOLUME II
Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972
VLADIMIR I. ARNOLD Collected Works
VOLUME II Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972
Edited by Alexander B. Givental Boris A. Khesin Alexander N. Varchenko Victor A. Vassiliev Oleg Ya. Viro
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Vladimir I. Arnold June 12, 1937 – June 3, 2010
Editors Alexander B. Givental Department of Mathematics University of California Berkeley, CA, USA
Victor A. Vassiliev Steklov Mathematical Institute Russian Academy of Sciences Moscow, Russia
Boris A. Khesin Department of Mathematics University of Toronto Toronto, ON, Canada
Oleg Ya. Viro Institute for Mathematical Sciences Stony Brook University Stony Brook, NY, USA
Alexander N. Varchenko Department of Mathematics University of North Carolina Chapel Hill, NC, USA
ISBN 978-3-642-31030-0 ISBN 978-3-642-31031-7 (ebook) DOI 10.1007/978-3-642-31031-7 Library of Congress Control Number: 2013937321 ¤ Springer-Verlag Berlin Heidelberg 2014 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This volume of the Collected Works appears in print after Vladimir Arnold's untimely death in June 2010. His passing was a terrible loss for mathematics and science in general. We hope that this project of Collected Works, which is needed now more than ever, will contribute to establishing the tremendous legacy of V.I. Arnold, a remarkable mathematician and human being. Some memories of V.I. Arnold can be found in the recent March and April 2012 issues of the Notices of the AMS. Our Editorial team has also suffered an unprecedented blow since Volume I was published in 2009. Jerry Marsden passed away in September 2010, and Vladimir Zakalyukin passed away in December 2011. We dedicate this volume to their memory. This Volume II of the Collected Works includes papers written by
