Nonlinear Dynamical Economics and Chaotic Motion
Usually, the first edition of a book still contains a multiplicity of typographic, con ceptional, and computational errors even if one believes the opposite at the time of publication. As this book did not represent a counterexample to this rule, the cur
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Nonlinear Dynamical Economics and Chaotic Motion Second, Revised and Enlarged Edition
With 133 Figures
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Dr. Hans-Walter Lorenz Volkswirtschaftliches Seminar Georg-August-Universitat G6ttingen Platz der G6ttinger Sieben 3 D-37073 G6ttingen, FRG
The first edition was published in 1989 as volume 334 of the series "Lecture Notes in Economics and Mathematical Systems".
ISBN-13:978-3-642-78326-5 e-ISBN-13:978-3-642-78324-1 DOT: 10.1007/978-3-642-78324-1 This work is subject to copyright. All rights are reserved, whether the whole or part ofthe material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication orparts thereofis only permitted under the provisions of the German Copyright Law of September 9,1965, in its version ofJune 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, 1993 Softcover reprint of the hardcover 2nd edition
1993
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 protective laws and regulations and therefore free for general use.
4217130-543210 - Printed on acid - free paper
To My Parents
... only nonlinear differential equations have interesting dynamics. M.
HIRSCH
(1984)
Unfortunately, many of the most important processes in nature are inherently nonlinear. R.L.
DEVANEY
(1992)
There are no true fractals in nature. (There are no true straight lines or circles either!) K
FALCONER
(1990)
Prefaces
Preface to the Second Edition Usually, the first edition of a book still contains a multiplicity of typographic, conceptional, and computational errors even if one believes the opposite at the time of publication. As this book did not represent a counterexample to this rule, the current second edition offers a chance to remove at least the known shortcomings. The book has been partly re-organized. The previously rather long Chapter 4 has been split into two separate chapters dealing with discrete-time and continuoustime approaches to nonlinear economic dynamics. The short summary of basic properties of linear dynamical systems has been banned to an appendix because the line of thought in the chapter seems to have been unnecessarily interrupted by these technical details and because the book concentrates on nonlinear systems. This appendix, which mainly deals with special formal properties of dynamical systems, also contains some new material on invariant subspaces and center-manifold reductions. A brief introduction into the theory of lags and operators is followed by a few remarks on the relation between the 'true' properties of dynamical systems and their behavior observable in numerical experiments. A
