Nonlinear Dynamical Economics and Chaotic Motion
The plan to publish the present book arose while I was preparing a joint work with Gunter Gabisch (Gabisch, G. /Lorenz, H. -W. : Business Cycle Theory. Berlin-Heidel berg-New York: Springer). It turned out that a lot of interesting material could only be
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Hans-Walter Lorenz
Nonlinear Dynamical Economics and Chaotic Motion
Lecture Notes in Economics and Mathematical Systems Managing Editors: M. Beckmann and W. Krelle
334 Hans-Walter Lorenz
Nonlinear Dynamical Economics and Chaotic Motion
Springer-Verlag Berlin Heidelberg GmbH
Editorial Board
H. Albach M. Beckmann (Managing Editor) P. Dhrymes G. Fandel G.Feichtinger J.Green W.Hildenbrand W.Krelle (Managing Editor) H. P. Kunzi K. Ritter R. Sato U. Schittko P. Schonfeld R. Selten Managing Editors
Prof. Dr. M. Beckmann Brown University Providence, Rl 02912, USA Prof. Dr. W. Krelle lnstitut fUr Gesellschafts- und Wirtschaftswissenschaften der Universitat Bonn Adenauerallee 24-42, D-5300 Bonn, FRG Author
Dr. Hans-Walter Lorenz Volkswirtschaftliches Seminar Georg-August-Universitat Gi:ittingen Platz der Gi:ittinger Sieben 3, D-3400 Gi:ittingen, FRG
ISBN 978-3-540-51413-8 ISBN 978-3-662-22233-1 (eBook) DOI 10.1007/978-3-662-22233-1
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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. ©Springer-Verlag Berlin Heidelberg 1989 Originally published by Springer-Verlag Berlin Heidelberg New York 1989 2142/3140-54321 0
To My Parents
... only nonlinear differential equations have interesting dynamics.
M. Hirsch ( 1984)
Preface
The plan to publish the present book arose while I was preparing a joint work with Gunter Gabisch (Gabisch, G./Lorenz, H.-W.: Business Cycle Theory. Berlin-Heidelberg-New York: Springer). It turned out that a lot of interesting material could only be sketched in a business cycle text, either because the relevance for business cycle theory was not evident or because the material required an interest in dynamical economics which laid beyond the scope of a survey text for advanced undergraduates. While much of the material enclosed in this book can be found in condensed and sometimes more or less identical form in that business cycle text, the present monograph attempts to present nonlinear dynamical economics in a broader context with economic examples from other fields than business cycle theory. It is a pleasure for me to acknowledge the critical comments, extremely detailed remarks, or suggestions by many friends and colleagues. The responses to earlier versions of the manuscript by W.A. Barnett, M. Boldrin, W.A. Brock, C. Chiarella, C. Dale, G. Feichtinger, P. Flaschel, D.K. Foley, R.M. Goodwin, D. Kelsey, M. Lines, A. Medio, L. Montrucchio, P. Read, C. Sayers, A. Schmutzler, H. Schnabl, G. Silverberg, H.-\'\!. Sinn, J. Sterman, and R. Tscherning not only encouraged me to publi
