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Author: Kung-Sik Chan Publisher: Springer Science & Business Media ISBN: 1475734646 Category : Mathematics Languages : en Pages : 312
Book Description
This book discusses dynamical systems that are typically driven by stochastic dynamic noise. It is written by two statisticians essentially for the statistically inclined readers. It covers many of the contributions made by the statisticians in the past twenty years or so towards our understanding of estimation, the Lyapunov-like index, the nonparametric regression, and many others, many of which are motivated by their dynamical system counterparts but have now acquired a distinct statistical flavor.
Author: Kung-Sik Chan Publisher: Springer Science & Business Media ISBN: 1475734646 Category : Mathematics Languages : en Pages : 312
Book Description
This book discusses dynamical systems that are typically driven by stochastic dynamic noise. It is written by two statisticians essentially for the statistically inclined readers. It covers many of the contributions made by the statisticians in the past twenty years or so towards our understanding of estimation, the Lyapunov-like index, the nonparametric regression, and many others, many of which are motivated by their dynamical system counterparts but have now acquired a distinct statistical flavor.
Author: Angelo Vulpiani Publisher: World Scientific ISBN: 9814277665 Category : Mathematics Languages : en Pages : 482
Book Description
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology. The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations. The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses. Sample Chapter(s). Introduction (164 KB). Chapter 1: First Encounter with Chaos (1,323 KB). Contents: First Encounter with Chaos; The Language of Dynamical Systems; Examples of Chaotic Behaviors; Probabilistic Approach to Chaos; Characterization of Chaotic Dynamical Systems; From Order to Chaos in Dissipative Systems; Chaos in Hamiltonian Systems; Chaos and Information Theory; Coarse-Grained Information and Large Scale Predictability; Chaos in Numerical and Laboratory Experiments; Chaos in Low Dimensional Systems; Spatiotemporal Chaos; Turbulence as a Dynamical System Problem; Chaos and Statistical Mechanics: Fermi-Pasta-Ulam a Case Study. Readership: Students and researchers in science (physics, chemistry, mathematics, biology) and engineering.
Author: Marco Thiel Publisher: Springer ISBN: 3642046290 Category : Science Languages : en Pages : 300
Book Description
This book is a collection of papers contributed by some of the greatest names in the areas of chaos and nonlinear dynamics. Each paper examines a research topic at the frontier of the area of dynamical systems. As well as reviewing recent results, each paper also discusses the future perspectives of each topic. The result is an invaluable snapshot of the state of the ?eld by some of the most important researchers in the area. The ?rst contribution in this book (the section entitled “How did you get into Chaos?”) is actually not a paper, but a collection of personal accounts by a number of participants of the conference held in Aberdeen in September 2007 to honour Celso Grebogi’s 60th birthday. At the instigation of James Yorke, many of the most well-known scientists in the area agreed to share their tales on how they got involved in chaos during a celebratory dinner in Celso’s honour during the conference. This was recorded in video, we felt that these accounts were a valuable historic document for the ?eld. So we decided to transcribe it and include it here as the ?rst section of the book.
Author: Rainer Klages Publisher: World Scientific ISBN: 9812565078 Category : Science Languages : en Pages : 458
Book Description
A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory.Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity.Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors.The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.
Author: Martin Golubitsky Publisher: Birkhäuser ISBN: 3034881673 Category : Technology & Engineering Languages : en Pages : 338
Book Description
The framework of ‘symmetry’ provides an important route between the abstract theory and experimental observations. The book applies symmetry methods to dynamical systems, focusing on bifurcation and chaos theory. Its exposition is organized around a wide variety of relevant applications. From the reviews: "[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS
Author: Stavros G. Stavrinides Publisher: Springer Nature ISBN: 3030354415 Category : Science Languages : en Pages : 169
Book Description
This book presents the proceedings of the “5th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems (CCS).” All Symposia in the series bring together scientists, engineers, economists and social scientists, creating a vivid forum for discussions on the latest insights and findings obtained in the areas of complexity, nonlinear dynamics and chaos theory, as well as their interdisciplinary applications. The scope of the latest Symposium was enriched with a variety of contemporary, interdisciplinary topics, including but not limited to: fundamental theory of nonlinear dynamics, networks, circuits, systems, biology, evolution and ecology, fractals and pattern formation, nonlinear time series analysis, neural networks, sociophysics and econophysics, complexity management and global systems.
Author: Edgar E. Peters Publisher: John Wiley & Sons ISBN: 9780471139386 Category : Business & Economics Languages : en Pages : 296
Book Description
The latest developments in chaos theory - from an industry expert Chaos and Order in the Capital Markets was the first book to introduce and popularize chaos as it applies to finance. It has since become the classic source on the topic. This new edition is completely updated to include the latest ripples in chaos theory with new chapters that tie in today's hot innovations, such as fuzzy logic, neural nets, and artificial intelligence. Critical praise for Peters and the first edition of Chaos and Order in the Capital Markets "The bible of market chaologists." - BusinessWeek "Ed Peters has written a first-class summary suitable for any investment professional or skilled investor." - Technical Analysis of Stocks & Commodities "It ranks among the most provocative financial books of the past few years. Reading this book will provide a generous payback for the time and mental energy expended." - Financial Analysts Journal This second edition of Chaos and Order in the Capital Markets brings the topic completely up to date with timely examples from today's markets and descriptions of the latest wave of technology, including genetic algorithms, wavelets, and complexity theory. Chaos and Order in the Capital Markets was the very first book to explore and popularize chaos theory as it applies to finance. It has since become the industry standard, and is regarded as the definitive source to which analysts, investors, and traders turn for a comprehensive overview of chaos theory. Now, this invaluable reference - touted by BusinessWeek as "the bible of market chaologists" - has been updated and revised to bring you the latest developments in the field. Mainstream capital market theory is based on efficient market assumptions, even though the markets themselves exhibit characteristics that are symptomatic of nonlinear dynamic systems. As it explores - and validates - this nonlinear nature, Chaos and Order repudiates the "random walk" theory and econometrics. It shifts the focus away from the concept of efficient markets toward a more general view of the forces underlying the capital market system. Presenting new analytical techniques, as well as reexamining methods that have been in use for the past forty years, Chaos and Order offers a thorough examination of chaos theory and fractals as applied to investments and economics. This new edition includes timely examples from today's markets and descriptions of cutting-edge technologies-genetic algorithms, wavelets, complexity theory-and hot innovations, such as fuzzy logic and artificial intelligence. Beyond the history of current capital market theory, Chaos and Order covers the crucial characteristics of fractals, the analysis of fractal time series through rescaled range analysis (R/S), the specifics of fractal statistics, and the definition and analysis of chaotic systems. It offers an in-depth exploration of: * Random walks and efficient markets - the development of the efficient market hypothesis (EMH) and modern portfolio theory * The linear paradigm - why it has failed * Nonlinear dynamic systems - phase space, the Henon Map, Lyapunov exponents * Applying chaos and nonlinear methods - neural networks, genetic algorithms * Dynamical analysis of time series - reconstructing a phase space, the fractal dimension Tonis Vaga's Coherent Market Hypothesis - the theory of social imitation, control parameters, Vaga's implementations Plus, Chaos and Order now contains a Windows-compatible disk including data sets for running analyses described in the appendices. Written by a leading expert in the field, Chaos and Order in the Capital Markets has all the information you need for a complete, up-to-date look at chaos theory. This latest edition will undoubtedly prove to be as invaluable as the first.
Author: Garnett Williams Publisher: CRC Press ISBN: 1482295415 Category : Mathematics Languages : en Pages : 518
Book Description
This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.
Author: G. Contopoulos Publisher: Springer Science & Business Media ISBN: 3540758267 Category : Science Languages : en Pages : 493
Book Description
The conference 'Chaos in Astronomy' was held in Athens on 17-20 Sept. 2007. This book contains edited refereed contributions. It offers an overview to students and newcomers entering various fields of dynamical astronomy.
Author: Kung-Sik Chan
Author: Kung-Sik Chan
Author: Kung-Sik Chan
Author: Angelo Vulpiani
Author: Marco Thiel
Author: Rainer Klages
Author: Martin Golubitsky
Author: Stavros G. Stavrinides
Author: Edgar E. Peters
Author: Garnett Williams
Author: G. Contopoulos