Classical Nonintegrability, Quantum Chaos With a contribution by Viv
Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. Th
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Classical Nonintegrabilrty, Quantum Chaos With a contribution by Viviane Baladi
Andreas Knauf Yakov G. Sinai
Springer Basel AG
Authors: Andreas Knauf Fachbereich 3 - Mathematik, M A 7-2 Technische Universität Berlin Straße des 17. Juni 135 10623 Berlin Germany
Yakov G. Sinai Department of Mathematics Princeton University Princeton, NJ 08544 USA e-mail: [email protected]
e-mail: [email protected] Viviane Baladi Section de Mathematiques Universite de Geneve CP 240 1211 Geneve 24 Switzerland e-mail: baladi @sc2a.unige.ch
1991 Mathematical Subject Classification 81Q50, 81U99, 58F11
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data Knauf, Andreas: Classical nonintegrability, quantum chaos / Andreas Knauf; Yakov G. Sinai. With a contribution by Viviane Baladi. - Basel ; Boston ; Berlin : Birkhäuser, 1997 (DMV-Seminar; Bd. 27) ISBN 978-3-7643-5708-5 ISBN 978-3-0348-8932-2 (eBook) DOI 10.1007/978-3-0348-8932-2 NE: Sinaj, Jakov G.:; Deutsche Mathematiker-Vereinigung: D M V Seminar
This work is subject to copyright. A l l rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use the permission of the copyright owner must be obtained. © 1997 Springer Basel A G Originally published by Birkhäuser Verlag, Basel, Switzerland in 1997 Camera-ready copy prepared by the author Printed on acid-free paper produced from chlorine-free pulp. TCF «> Cover design: Heinz Hiltbrunner, Basel I S B N 978-3-7643-5708-5
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Contents 1 Introduction ...........................................................
1
2 Dynamical Zeta Functions .............................................
3
2.1
Introduction and Motivation......................................
3
2.1.1 Transfer Operators.................................... ...... 2.1.2 Invariant Function Spaces ................................... 2.1.3 Quasicompactness ........................................... 2.1.4 Weighted Dynamical Zeta Functions.........................
3 4 5 7
Commented Bibliography .........................................
9
2.2.0 Foundations .................................................. 2.2.1 Surveys ..................................................... 2.2.2 Applications ........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Subshifts of Finite Type and Axiom A ....................... 2.2.4 The Smooth Expanding Case ................................ 2.2.5 The Smooth Hyperbolic Case ................................ 2.2.6 The One-dimensional Case .................................. 2.2.7 The One-dimensional Case: Kneading Operator Approach....
9 9 10 10 11 12 13 14
3 Irregular Scattering ...................................................
21
2.2
3.1
Notions of Classical Potential S
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