[PDF] Dynamique Non Lineaire Et Le Chaos eBook

Author : Ralph Abraham
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 20,29 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 1461219361

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The materials in the book and on the accompanying disc are not solely developed with only the researcher and professional in mind, but also with consideration for the student: most of this material has been class-tested by the authors. The book is packed with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-colour animations tied directly to the subject matter of the book itself. The cross-platform CD also contains the program ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided to allow readers to work directly with the code from which the graphics in the book were taken.

Author : Bertrand Duplantier
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 26,7 MB
Release : 2013-11-26
Category : Mathematics
ISBN : 3034806973

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This twelfth volume in the Poincaré Seminar Series presents a complete and interdisciplinary perspective on the concept of Chaos, both in classical mechanics in its deterministic version, and in quantum mechanics. This book expounds some of the most wide ranging questions in science, from uncovering the fingerprints of classical chaotic dynamics in quantum systems, to predicting the fate of our own planetary system. Its seven articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a complete description by the mathematician É. Ghys of the paradigmatic Lorenz attractor, and of the famed Lorenz butterfly effect as it is understood today, illuminating the fundamental mathematical issues at play with deterministic chaos; a detailed account by the experimentalist S. Fauve of the masterpiece experiment, the von Kármán Sodium or VKS experiment, which established in 2007 the spontaneous generation of a magnetic field in a strongly turbulent flow, including its reversal, a model of Earth’s magnetic field; a simple toy model by the theorist U. Smilansky – the discrete Laplacian on finite d-regular expander graphs – which allows one to grasp the essential ingredients of quantum chaos, including its fundamental link to random matrix theory; a review by the mathematical physicists P. Bourgade and J.P. Keating, which illuminates the fascinating connection between the distribution of zeros of the Riemann ζ-function and the statistics of eigenvalues of random unitary matrices, which could ultimately provide a spectral interpretation for the zeros of the ζ-function, thus a proof of the celebrated Riemann Hypothesis itself; an article by a pioneer of experimental quantum chaos, H-J. Stöckmann, who shows in detail how experiments on the propagation of microwaves in 2D or 3D chaotic cavities beautifully verify theoretical predictions; a thorough presentation by the mathematical physicist S. Nonnenmacher of the “anatomy” of the eigenmodes of quantized chaotic systems, namely of their macroscopic localization properties, as ruled by the Quantum Ergodic theorem, and of the deep mathematical challenge posed by their fluctuations at the microscopic scale; a review, both historical and scientific, by the astronomer J. Laskar on the stability, hence the fate, of the chaotic Solar planetary system we live in, a subject where he made groundbreaking contributions, including the probabilistic estimate of possible planetary collisions. This book should be of broad general interest to both physicists and mathematicians.

Author : Christophe Letellier
Publisher : World Scientific
Page : 362 pages
File Size : 34,11 MB
Release : 2013
Category : Science
ISBN : 9814434868

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The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto RAssler, Ren(r) Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical OCo not necessarily widely known OCo contributions (about the different types of chaos introduced by RAssler and not just the RAssler attractor; Gumowski and Mira's contributions in electronics; Poincar(r)'s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology,

Author : Dr Paul R. Fleischman
Publisher : Pariyatti
Page : 194 pages
File Size : 34,69 MB
Release : 2021-11-15
Category : Philosophy
ISBN : 1681724154

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Nous n'avons jamais eu autant besoin des bénéfices thérapeutiques à retirer d'une meilleure conscience de soi que dans le monde d'aujourd'hui, dans toute sa complexité. Tout au long de sept essais poétiques et passionnants, le Dr Fleischman explore les connections existant entre la psychiatrie, la science et la méditation. Il s'agit d'une nouvelle traduction de ce livre achevée en 2021.

Author : Ralph Abraham
Publisher : World Scientific
Page : 231 pages
File Size : 18,15 MB
Release : 2000
Category : Mathematics
ISBN : 9810244045

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This book is an authoritative and unique reference for the history of chaos theory, told by the pioneers themselves. It also provides an excellent historical introduction to the concepts. There are eleven contributions, and six of them are published here for the first time ? two by Steve Smale, three by Yoshisuke Ueda, and one each by Ralph Abraham, Edward Lorenz, Christian Mira, Floris Takens, T Y Li and James A Yorke, and Otto E Rossler.

Author : A. Albert
Publisher : IOS Press
Page : 416 pages
File Size : 18,63 MB
Release : 1995
Category : Computers
ISBN : 9789051992144

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This publication reflects on the discussion on using chaos theory for the study of society. It explores the interface between chaos theory and the social sciences. A broad variety of fields (including Sociology, Anthropology, Economics, Political Science, Management, Philosophy and Cognitive Sciences) is represented in the book. The leading themes are: Conceptual and Methodological Issues, Social Connectionism and the Connectionist Mind, Social Institutions and Public Policy, and Social Simulations. The book includes the following topics: the relevance of the complexity-chaos paradigm for analyzing social systems, the usefulness of nonlinear dynamics for studying the formation and sustainability of social groups, the comparison between spontaneous social orders and spontaneous biological/natural orders, the building of Artificial Societies, and the contribution of the chaos paradigm to a better understanding and formulation of public policies.