Complex and Chaotic Nonlinear Dynamics Advances in Economics and Fin
Complex dynamics constitute a growing and increasingly important area as they offer a strong potential to explain and formalize natural, physical, financial and economic phenomena. This book pursues the ambitious goal to bring together an extensive body o
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Complex and Chaotic Nonlinear Dynamics Advances in Economics and Finance, Mathematics and Statistics
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Complex and Chaotic Nonlinear Dynamics
Thierry Vialar
Complex and Chaotic Nonlinear Dynamics Advances in Economics and Finance, Mathematics and Statistics
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Dr. Thierry Vialar University of Paris X Dept. of Economics 200, ave de la République 92001 Nanterre Cedex France www.isnld.com [email protected]
ISBN 978-3-540-85977-2
Pr. Alain Goergen École normale supérieure de Cachan Dept. of Economics 61, ave du Président Wilson 94235 Cachan Cedex France
e-ISBN 978-3-540-85978-9
Library of Congress Control Number: 2008937818 c 2009 Springer-Verlag Berlin Heidelberg 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.com
To Mr. Professor Alain GOERGEN with my deep gratitude and admiration.
Preface
Since the 1970s, Complex and chaotic nonlinear dynamics (in short, Complex Dynamics) constitute a growing and increasingly important area that comprises advanced research activities and strongly interdisciplinary approaches. This area is of a fundamental interest in many sciences, including Economics. Let us start with a comment about the interest of Complex Dynamics in Economics and in so doing the necessity of such a book and its interdisciplinarity: Mathematics in Economics have a very strong didactic role. Mathematics state theoretical models and paradigms that must conform to measurements. However, in Economics the measurements are rare, more often of a small number of points and of a very low density, except for stock markets. This chasm that separates Economics from the “dense” measurable reality has maintained economists in a kind of “isolation” (compared with other sciences): (1) that of the qualitative approach that can be conducted, for instance, in a literary way, very often of great relevance but which is not quantitative, (2) and that of the construction of models (“mathematical idealities”) with a strong didactic or mechanistic vocation often far from the richness of “the living”. This is above all a problem of measurement. Beyond the epistemological revolution of nonlinear theory, today there is that of the information systems an
