Critical Phenomena in Natural Sciences Chaos, Fractals, Selforga
Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large varia
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rgetics Series Editor Hermann Haken ¨r Theoretische Physik Institut fu und Synergetik der Universit¨at Stuttgart 70550 Stuttgart, Germany and Center for Complex Systems Florida Atlantic University Boca Raton, FL 33431, USA
Members of the Editorial Board Åke Andersson, Stockholm, Sweden Gerhard Ertl, Berlin, Germany Bernold Fiedler, Berlin, Germany Yoshiki Kuramoto, Sapporo, Japan J¨ urgen Kurths, Potsdam, Germany Luigi Lugiato, Milan, Italy J¨ urgen Parisi, Oldenburg, Germany Peter Schuster, Wien, Austria Frank Schweitzer, Z¨ urich, Switzerland Didier Sornette, Z¨ urich, Switzerland, and Nice, France Manuel G. Velarde, Madrid, Spain SSSyn – An Interdisciplinary Series on Complex Systems The success of the Springer Series in Synergetics has been made possible by the contributions of outstanding authors who presented their quite often pioneering results to the science community well beyond the borders of a special discipline. Indeed, interdisciplinarity is one of the main features of this series. But interdisciplinarity is not enough: The main goal is the search for common features of self-organizing systems in a great variety of seemingly quite different systems, or, still more precisely speaking, the search for general principles underlying the spontaneous formation of spatial, temporal or functional structures. The topics treated may be as diverse as lasers and fluids in physics, pattern formation in chemistry, morphogenesis in biology, brain functions in neurology or self-organization in a city. As is witnessed by several volumes, great attention is being paid to the pivotal interplay between deterministic and stochastic processes, as well as to the dialogue between theoreticians and experimentalists. All this has contributed to a remarkable cross-fertilization between disciplines and to a deeper understanding of complex systems. The timeliness and potential of such an approach are also mirrored – among other indicators – by numerous interdisciplinary workshops and conferences all over the world.
Didier Sornette
Critical Phenomena in Natural Sciences Chaos, Fractals, Selforganization and Disorder: Concepts and Tools
Second Edition With 102 Figures
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Professor Didier Sornette Chair of Entrepreneurial Risks Department of Management, Technology and Economics (D-MTEC) ETH Zentrum 8092 Zürich, Switzerland and Laboratoire de Physique de la Matière Condens´ee CNRS UMR6622 Université de Nice-Sophia Antipolis Faculté des Sciences, B.P. 71 06108 Nice Cedex 2, France
Library of Congress Control Number: 2006920906
2nd Printing of the Hardcover Edition with ISBN 3-540-40754-5 ISSN 0172-7389 ISBN-10 3-540-30882-2 2nd Edition Springer Berlin Heidelberg New York ISBN-13 978-3-540-30882-9 2nd Edition Springer Berlin Heidelberg New York 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.
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