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A reference for the history of chaos theory, told by the pioneers themselves, and eleven other authoritative contributions. Provides a historical introduction to all of the concepts of chaos theory. ... Read more

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Neuroscience was the topic of several talks and papers. Emerging themes appear to be the control of neuronal activity and the construction of hybrid neuron-circuit systems, and that of using nonlinear data analysis techniques for the characterization of physiological pathologies. It was shown that these approaches can be applied to cardiac arrhythmias and detection of problems in EEG signals. Synchronization of chaos in optical systems was also presented. New topics that were presented were Ecology and Traffic dynamics. Also, ecological dynamics showed that state space concepts can also be applied to populations and insect networks. Topics include: Chemistry, Electronics, Geophysics and Astrophysics, Neuroscience and Physiology, Data Analysis, Applications, Traffic, Combustion, Optics, Hydrodynamics, Condensed Matter, Synchrony, Dynamo, and Ecology.

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Contains papers by the invited speakers at the NATO sponsored workshop on noise and chaos in nonlinear dynamical systems held in Turin in March 1989. The conference was divided into three main parts: optics, statistical mechanics, and chaos. ... Read more

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Since 1972 the Schools on Nonlinear Physics in Gorky have been a meeting place for Soviet Scientists working in this field. Since 1989 the proceedings appear in English. They present a good cross section of nonlinear physics in the USSR. This third volume emerged from material presented at the 1989 School. It contains sections dealing with nonlinear problems in physics and astrophysics, quantum and solid state physics, dynamical chaos and self-organization. ... Read more

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This text focuses on the promotion and accelerated application of dynamics, chaotic and other advanced signal processing techniques in engineering and the sciences. Major topics covered include: nonlinear time series analysis and the processing and synthesis of chaotic signals; applications in the control of chaos; and advanced information theoretic techniques for identifying nonlinearities in data structure. This book should be of use to engineers and scientists in signal processing interested in nonlinear signal analysis as well as scientists performing turbulence research and analysis. ... Read more

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Written in Alwyn Scott’s inimitable style, one that readers will find both lucid and accessible, this masterwork elucidates the explosion of activity in nonlinear science in recent decades. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science is essential for understanding the scientific developments of the twenty-first century.

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Like relativity and quantum theory chaos research is another prominent concept of 20th century physics that has triggered deep and far-reaching discussions in the philosophy of science. In this volume outstanding scientists discuss the fundamental problems of the concepts of law and of prediction. They present their views in their contributions to this volume, but they also are exposed to criticism in transcriptions of recordings made during discussions and in comments on their views also published in this book. Although all authors assume familiarity with some background in physics they also address the philosophers of science and even a general audience interested in modern science's contribution to a deeper understanding of reality. ... Read more

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These papers examine topics in nonlinear science, such as the status of KAM theory from a physicist's point of view, the numerical study of the approach to equilibrium in the Henon-Heiles model and chaotic dynamics in the Maxwell-Bloch equation. ... Read more

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The Maslov Classes have been playing an essential role in various parts of applied and pure mathematics, and physics, since the early 70's. Their correct definition is due to V. I. Arnold and J. Leray, in the transversal case, and to P. Dazord and the author in the general case. The aim of this book is to give a thorough treatment of the theory of the Maslov classes and of their relationship with the metaplectic group. It is (among other things) shown that these classes can be reconstructed, modulo 4, using only the analytic properties of the metaplectic group. In the last chapter the author sketches a scheme for geometric quantization by introducing two new concepts, that of metaplectic half-form and that of Lagrangian catalogue, the latter generalizes and simplifies the notion of "Lagrangian function" introduced by J. Leray. A Lagrangian catalogue is a collection of metaplectic half-forms which are themselves "cohomological wave functions", whose definition is made possible by using the combinatorial properties of the Maslov classes. The transformation of Lagrangian catalogues under the metaplectic group and of Hamiltonian flows is studied, and it is shown that one thus recovers very easily the so-called "quasi-classical approximation" to the solutions of Schrödinger equation if one introduces a natural concept, that of projection of a Lagrangian catalogue. An application to geometric phase shifts, including Berry's phase, is given.

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Breadth of scope is unique

Author is a widely-known and successful textbook author

Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas

No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples

Includes a section on cellular automata

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A new class of insulating solids was recently discovered. When irradiated by a few visible photons, these solids give rise to a macroscopic excited domain that has new structural and electronic orders quite different from the starting ground state. This occurrence is called "photoinduced phase transition", and this multi-authored book reviews recent theoretical and experimental studies of this new phenomenon.

Why and how do photoexcited few electrons finally result in an excited domain with a macroscopic size? How is the resultant photoinduced phase different from the ordinary thermal-induced phase? This review volume answers those essential questions. ... Read more

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This volume is dedicated to John Hammersley, one of the most influential of all researchers in random phenomena.It provides a unique survey of the current state of mathematical research in this field, which has seen great advances in recent decades.As Hammersley's colleagues and collaborators, the contributors are all leading figures in their respective fields..They describe progress in such areas as percolation theory, random networks, lattice animals, stochastic geometry, diffusions, covering problems, Monte Carlo methods, and operations research. Computational complexity, random fields, convergence on random variables, classical and quantum mechanics, and analytic number theory are also covered.Researchers and graduate students in a variety of disciplines will find this an authoritative and up-to-date survey of many of the most exciting developments in mathematics today. ... Read more

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Self-organized criticality (SOC) has become a magic word in various scientific disciplines; it provides a framework for understanding complexity and scale invariance in systems showing irregular fluctuations. In the first 10 years after Per Bak and his co-workers presented their seminal idea, more than 2000 papers on this topic appeared. Seismology has been a field in earth sciences where the SOC concept has already deepened the understanding, but there seem to be much more examples in earth sciences where applying the SOC concept may be fruitful. After introducing the reader into the basics of fractals, chaos and SOC, the book presents established and new applications of SOC in earth sciences, namely earthquakes, forest fires, landslides and drainage networks. ... Read more