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: 457

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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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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: 1656

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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: 6134

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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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Dimension Estimation and Models

Author: Howell Tong

Publisher: World Scientific

ISBN: 9789810213534

Category: Mathematics

Page: 223

View: 2147

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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: 3372

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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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E.E. Slutsky as Economist and Mathematician

Crossing the Limits of Knowledge

Author: Vincent Barnett

Publisher: Routledge

ISBN: 1136737316

Category: Business & Economics

Page: 224

View: 9295

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E.E. Slutsky is perhaps the Russian/Ukrainian economist most quoted by mainstream economists today. This is the first research monograph to examine the life and work of the internationally-renowned economist and mathematician. It does so from both a ‘history of economics’ perspective and a ‘history of science’ perspective, bringing these two strands together in order to demonstrate Slutsky’s enduring legacy as an innovative researcher and an influential intellectual. It also presents some of Slutsky’s lesser-known (and hitherto-unavailable) works in English translation.
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Mathematical Methods for Analysis of a Complex Disease

Author: F. C. Hoppensteadt

Publisher: American Mathematical Soc.

ISBN: 0821872869

Category: Mathematics

Page: 149

View: 2092

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Complex diseases involve most aspects of population biology, including genetics, demographics, epidemiology, and ecology. Mathematical methods, including differential, difference, and integral equations, numerical analysis, and random processes, have been used effectively in all of these areas. The aim of this book is to provide sufficient background in such mathematical and computational methods to enable the reader to better understand complex systems in biology, medicine, and the life sciences. It introduces concepts in mathematics to study population phenomena with the goal of describing complicated aspects of a disease, such as malaria, involving several species. The book is based on a graduate course in computational biology and applied mathematics taught at the Courant Institute of Mathematical Sciences in fall 2010. The mathematical level is kept to essentially advanced undergraduate mathematics, and the results in the book are intended to provide readers with tools for performing more in-depth analysis of population phenomena.
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The Chaos Theory of Careers

A New Perspective on Working in the Twenty-First Century

Author: Robert Pryor,Jim Bright

Publisher: Routledge

ISBN: 113523129X

Category: Business & Economics

Page: 256

View: 7178

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The Chaos Theory of Careers outlines the application of chaos theory to the field of career development. It draws together and extends the work that the authors have been doing over the last 8 to 10 years. This text represents a new perspective on the nature of career development. It emphasizes the dimensions of careers frequently neglected by contemporary accounts of careers such as the challenges and opportunities of uncertainty, the interconnectedness of current life and the potential for information overload, career wisdom as a response to unplanned change, new approaches to vocational assessment based on emergent thinking, the place of spirituality and the search for meaning and purpose in, with and through work, the integration of being and becoming as dimensions of career development. It will be vital reading for all those working in and studying career development, either at advanced undergraduate or postgraduate level and provides a new and refreshing approach to this fast changing subject. Key themes include: Factors such as complexity, change, and contribution People's aspirations in relation to work and personal fulfilment Contemporary realities of career choice, career development and the working world
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Theoretical Concepts in Physics

An Alternative View of Theoretical Reasoning in Physics

Author: Malcolm S. Longair,Professor Malcolm S Longair

Publisher: Cambridge University Press

ISBN: 9780521528788

Category: Science

Page: 569

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A novel and integrated approach to physics, covering background history, basic tools and modern techniques.
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