Geodesic and Horocyclic Trajectories
During the past thirty years, strong relationships have interwoven the fields of dynamical systems, linear algebra and number theory. This rapport between different areas of mathematics has enabled the resolution of some important conjectures and has in f
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Françoise Dal’Bo
Geodesic and Horocyclic Trajectories
Françoise Dal’Bo IRMAR Université Rennes 1 Rennes Cedex France [email protected] Editorial board: Sheldon Axler, San Francisco State University Vincenzo Capasso, Universitá degli Studi di Milano Carles Casacuberta, Universitat de Barcelona Angus Macintyre, Queen Mary, University of London Kenneth Ribet, University of California, Berkeley Claude Sabbah, CNRS, École Polytechnique Endre Süli, University of Oxford Wojbor Woyczynski, Case Western Reserve University Translation from the French language edition: Trajectoires géodésiques et horocycliques by Françoise Dal’Bo EDP Sciences ISBN 978-2-86883-997-8 c 2007 EDP Sciences, CNRS Editions, France. Copyright http://www.edpsciences.org/ http://www.cnrseditions.fr/ All Rights Reserved ISBN 978-0-85729-072-4 e-ISBN 978-0-85729-073-1 DOI 10.1007/978-0-85729-073-1 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Control Number: 2010937998 Mathematics Subject Classification (2010): 37Bxx, 11Jxx, 20H10, 37D40, 11A55 c Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of 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 laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Dominique, to Alma and Romance
Preface
In this text, we present an introduction to the topological dynamics of two classical flows associated with surfaces of curvature −1, namely the geodesic and horocycle flows. Since the end of the nineteenth century, many texts have been written on this subject. Why have we undertaken this project? In the course of several talks that we have given on this topic, notably during some summer workshops which were organized by the University of Savoie, we have often regretted not being able to recommend a book to those who wanted to find out about this area for themselves. Due to their determination and their enthu
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