Dynamique Non-linéaire Et Le Chaos PDF Download

Author:
Publisher:
ISBN:
Category : Chaotic behavior in systems
Languages : en
Pages : 130

View

Book Description

Author: Ralph Abraham
Publisher: Springer Science & Business Media
ISBN: 9780387943008
Category : Computers
Languages : en
Pages : 282

View

Book Description
Chaos Theory is a synonym for dynamical systems theory, a branch of mathematics. Dynamical systems come in three flavors: flows (continuous dynamical systems), cascades (discrete, reversible, dynamical systems), and semi-cascades (discrete, irreversible, dynamical systems). Flows and semi-cascades are the classical systems iuntroduced by Poincare a centry ago, and are the subject of the extensively illustrated book: "Dynamics: The Geometry of Behavior," Addison-Wesley 1992 authored by Ralph Abraham and Shaw. Semi- cascades, also know as iterated function systems, are a recent innovation, and have been well-studied only in one dimension (the simplest case) since about 1950. The two-dimensional case is the current frontier of research. And from the computer graphcis of the leading researcher come astonishing views of the new landscape, such as the Julia and Mandelbrot sets in the beautiful books by Heinz-Otto Peigen and his co-workers. Now, the new theory of critical curves developed by Mira and his students and Toulouse provide a unique opportunity to explain the basic concepts of the theory of chaos and bifurcations for discete dynamical systems in two-dimensions. The materials in the book and on the accompanying disc are not solely developed only with the researcher and professional in mind, but also with consideration for the student. The book is replete with some 100 computer graphics to illustrate the material, and the CD-ROM contains full-color animations that are tied directly into the subject matter of the book, itself. In addition, much of this material has also been class-tested by the authors. The cross-platform CD also contains a software program called ENDO, which enables users to create their own 2-D imagery with X-Windows. Maple scripts are provided which give the reader the option of working directly with the code from which the graphcs in the book were

Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 568

View

Book Description

Author: Luciano Boi
Publisher: Peter Lang
ISBN: 9783039107629
Category : Philosophy
Languages : fr
Pages : 324

View

Book Description
Cet ouvrage aborde des questions fondamentales qui se rattachent à des idées et des méthodes développées depuis quelques décennies dans les sciences de la nature et du vivant ainsi qu'à l'interface entre les deux. Il propose de nouvelles approches interdisciplinaires pour étudier plusieurs aspects théoriques, empiriques, et épistémologiques qui touchent à des problèmes scientifiques cruciaux pour lesquels on ne dispose pas à l'heure actuelle d'explication satisfaisante. Ces questions et ces problèmes concernent notamment la signification des symétries, des brisures de symétries et de la complexité dans la nature et le monde du vivant, le statut des systèmes dynamiques, des bifurcations et du chaos, les propriétés de stabilité et d'instabilité des structures ainsi que la nature des processus sous-jacents à l'émergence des formes et à l'apparition de comportements coopératifs. Dans ce livre on trouvera maints exemples qui illustrent comment la géométrie et la topologie offrent une conception dynamique de la nature qui ne sépare plus à la hache et de manière absolue le vivant de la matière dite inerte, l'ordre du désordre, le simple du complexe, le local du global, la stabilité de l'instabilité, le déterminisme de l'indéterminisme, le certain de l'aléatoire, etc. Cet ouvrage met en relation la diversité étonnante des phénomènes et des formes que l'on rencontre dans la nature et que l'on observe dans le monde biologique avec les différents modes selon lesquels les corps physiques et les êtres vivants, et tout particulièrement leurs substrats physico-chimiques, sont sujets à une transformation incessante sous l'action de quelques grands principes spatiaux et temporels.

Author: North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 62

View

Book Description

Author: Christophe Letellier
Publisher: World Scientific
ISBN: 9814434868
Category : Science
Languages : en
Pages : 362

View

Book Description
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: Ralph Abraham
Publisher: World Scientific
ISBN: 9810244045
Category : Mathematics
Languages : en
Pages : 231

View

Book Description
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: Bertrand Duplantier
Publisher: Springer Science & Business Media
ISBN: 3034806973
Category : Mathematics
Languages : en
Pages : 281

View

Book Description
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: Ralph Abraham
Publisher: World Scientific
ISBN: 9814492469
Category : Science
Languages : en
Pages : 231

View

Book Description
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: North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 130

View

Book Description