Laws of Chaos

Invariant Measures and Dynamical Systems in One Dimension

Author: Abraham Boyarsky,Pawel Gora

Publisher: Springer Science & Business Media

ISBN: 1461220246

Category: Mathematics

Page: 400

View: 1226

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A hundred years ago it became known that deterministic systems can exhibit very complex behavior. By proving that ordinary differential equations can exhibit strange behavior, Poincare undermined the founda tions of Newtonian physics and opened a window to the modern theory of nonlinear dynamics and chaos. Although in the 1930s and 1940s strange behavior was observed in many physical systems, the notion that this phenomenon was inherent in deterministic systems was never suggested. Even with the powerful results of S. Smale in the 1960s, complicated be havior of deterministic systems remained no more than a mathematical curiosity. Not until the late 1970s, with the advent of fast and cheap comput ers, was it recognized that chaotic behavior was prevalent in almost all domains of science and technology. Smale horseshoes began appearing in many scientific fields. In 1971, the phrase 'strange attractor' was coined to describe complicated long-term behavior of deterministic systems, and the term quickly became a paradigm of nonlinear dynamics. The tools needed to study chaotic phenomena are entirely different from those used to study periodic or quasi-periodic systems; these tools are analytic and measure-theoretic rather than geometric. For example, in throwing a die, we can study the limiting behavior of the system by viewing the long-term behavior of individual orbits. This would reveal incomprehensibly complex behavior. Or we can shift our perspective: Instead of viewing the long-term outcomes themselves, we can view the probabilities of these outcomes. This is the measure-theoretic approach taken in this book.
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Chaos Theory

Modeling, Simulation and Applications : Selected Papers from the 3rd Chaotic Modeling and Simulation Conference (CHAOS2010), Chania, Crete, Greece, 1-4 June 2010

Author: Charilaos Skiadas,Ioannis Dimotikalis

Publisher: World Scientific

ISBN: 9814350346

Category: Chaotic behavior in systems

Page: 450

View: 1721

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The work done in chaotic modeling and simulation during the last decades has changed our views of the world around us and has introduced new scientific tools, methods and techniques. Advanced topics of these achievements are included in this volume on Chaos Theory which focuses on Chaotic Modeling, Simulation and Applications of the nonlinear phenomena. This volume includes the best papers presented in the 3rd International Conference on CHAOS. This interdisciplinary conference attracted people from many scientific fields dealing with chaos, nonlinear dynamics, fractals and the works presented and the papers included here are of particular interest that could provide a broad understanding of chaos in its various forms. The chapters relate to many fields of chaos including Dynamical and Nonlinear Systems, Attractors and Fractals, Hydro-Fluid Dynamics and Mechanics, Chaos in Meteorology and Cosmology, Chaos in Biology and Genetics, Chaotic Control, Chaos in Economy and Markets, and Computer Composition and Chaotic Simulations, including related applications.
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Computational Science and Its Applications – ICCSA 2009

International Conference, Seoul, Korea, June 29--July 2, 2009, Proceedings

Author: Osvaldo Gervasi,David Taniar,Beniamino Murgante,Antonio Laganà,Youngsong Mun

Publisher: Springer Science & Business Media

ISBN: 3642024572

Category: Computers

Page: 957

View: 8244

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The two-volume set LNCS 5592 and 5593 constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2009, held in Seoul, Korea, in June/July, 2009. The two volumes contain papers presenting a wealth of original research results in the field of computational science, from foundational issues in computer science and mathematics to advanced applications in virtually all sciences making use of computational techniques. The topics of the fully refereed papers are structured according to the five major conference themes: computational methods, algorithms and scientific applications, high performance technical computing and networks, advanced and emerging applications, as well as information systems and information technologies. Moreover, submissions from more than 20 workshops and technical sessions contribute to this publication.These cover topics such as geographical analysis, urban modeling, spatial statistics, wireless and ad hoc networking, logical, scientific and computational aspects of pulse phenomena in transitions, high-performance computing and information visualization, sensor network and its applications, molecular simulations structures and processes, collective evolutionary systems, software engineering processes and applications, molecular simulations structures and processes, internet communication security, security and privacy in pervasive computing environments, and mobile communications.
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Basic Principles and Applications of Probability Theory

Author: Valeriy Skorokhod

Publisher: Springer Science & Business Media

ISBN: 9783540263128

Category: Mathematics

Page: 282

View: 9906

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The book is an introduction to modern probability theory written by one of the famous experts in this area. Readers will learn about the basic concepts of probability and its applications, preparing them for more advanced and specialized works.
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From Cardinals to Chaos

Reflection on the Life and Legacy of Stanislaw Ulam

Author: N. G. Cooper,Roger Eckhardt,Nancy Shera

Publisher: CUP Archive

ISBN: 9780521367349

Category: Science

Page: 318

View: 9769

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First published 1987 as Los Alamos science, special issue. A compendium of biographical (and autobiographical) notes, essays, and scientific articles reflecting on Ulam's legacy of interdisciplinary approaches to problems in math, physics, and biology; and previously unpublished miscellanea--conversations, a satirical play. The whole serves to celebrate the personality and contributions of the dynamic mathematician. Annotation copyrighted by Book News, Inc., Portland, OR
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Nonlinear Mathematics for Uncertainty and its Applications

Author: Shoumei Li,Xia Wang,Yoshiaki Okazaki,Jun Kawabe,Toshiaki Murofushi,Li Guan

Publisher: Springer Science & Business Media

ISBN: 364222833X

Category: Computers

Page: 709

View: 4890

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This volume is a collection of papers presented at the international conference on Nonlinear Mathematics for Uncertainty and Its Applications (NLMUA2011), held at Beijing University of Technology during the week of September 7--9, 2011. The conference brought together leading researchers and practitioners involved with all aspects of nonlinear mathematics for uncertainty and its applications. Over the last fifty years there have been many attempts in extending the theory of classical probability and statistical models to the generalized one which can cope with problems of inference and decision making when the model-related information is scarce, vague, ambiguous, or incomplete. Such attempts include the study of nonadditive measures and their integrals, imprecise probabilities and random sets, and their applications in information sciences, economics, finance, insurance, engineering, and social sciences. The book presents topics including nonadditive measures and nonlinear integrals, Choquet, Sugeno and other types of integrals, possibility theory, Dempster-Shafer theory, random sets, fuzzy random sets and related statistics, set-valued and fuzzy stochastic processes, imprecise probability theory and related statistical models, fuzzy mathematics, nonlinear functional analysis, information theory, mathematical finance and risk managements, decision making under various types of uncertainty, and others.
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From Cosmos to Chaos

The Science of Unpredictability

Author: Peter Coles

Publisher: Oxford University Press on Demand

ISBN: 0198567626

Category: Mathematics

Page: 216

View: 7714

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Looks at the role of probability in modern science. Using the developments in fundamental physics as examples, this book shows how central is the need to deal with uncertainty and incomplete knowledge. It also covers developments in physics, such as superstrings and dark energy, and draws lessons for everyday life.
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Dimension Estimation and Models

Author: Howell Tong

Publisher: World Scientific

ISBN: 9789810213534

Category: Mathematics

Page: 223

View: 9672

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This volume is the first in the new series Nonlinear Time Series and Chaos. The general aim of the series is to provide a bridge between the two communities by inviting prominent researchers in their respective fields to give a systematic account of their chosen topics, starting at the beginning and ending with the latest state. It is hoped that researchers in both communities will find the topics relevant and thought provoking. In this volume, the first chapter, written by Professor Colleen Cutler, is a comprehensive account of the theory and estimation of fractal dimension, a topic of central importance in dynamical systems, which has recently attracted the attention of the statisticians. As it is natural to study a stochastic dynamical system within the framework of Markov chains, it is therefore relevant to study their limiting behaviour. The second chapter, written by Professor Kung-Sik Chan, reviews some limit theorems of Markov chains and illustrates their relevance to chaos. The next three chapters are concerned with specific models. Briefly, Chapter Three by Professor Peter Lewis and Dr Bonnie Ray and Chapter Four by Professor Peter Brockwell generalise the class of self-exciting threshold autoregressive models in different directions. In Chapter Three, the new and powerful methodology of multivariate adaptive regression splines (MARS) is adapted to time series data. Its versatility is illustrated by reference to the very interesting and complex sea surface temperature data. Chapter Four exploits the greater tractability of continuous-time Markov approach to discrete-time data. The approach is particularly relevant to irregularly sampled data. The concluding chapter, by Professor Pham Dinh Tuan, is likely to be the most definitive account of bilinear models in discrete time to date.
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Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition

Author: N.A

Publisher: ScholarlyEditions

ISBN: 1490107509

Category: Mathematics

Page: 1037

View: 9082

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Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Approximation Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Approximation Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
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The Logistic Map and the Route to Chaos

From the Beginnings to Modern Applications

Author: Marcel Ausloos,Michel Dirickx

Publisher: Springer Science & Business Media

ISBN: 3540320237

Category: Science

Page: 413

View: 548

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Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology. Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of the developments initiated by Verhulst over a century ago.
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