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Author: Heinz Georg Schuster
Publisher: John Wiley & Sons
ISBN: 3527606416
Category : Science
Languages : en
Pages : 312
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Book Description
A new edition of this well-established monograph, this volume provides a comprehensive overview over the still fascinating field of chaos research. The authors include recent developments such as systems with restricted degrees of freedom but put also a strong emphasis on the mathematical foundations. Partly illustrated in color, this fourth edition features new sections from applied nonlinear science, like control of chaos, synchronisation of nonlinear systems, and turbulence, as well as recent theoretical concepts like strange nonchaotic attractors, on-off intermittency and spatio-temporal chaotic motion.
Author: Heinz Georg Schuster
Publisher: John Wiley & Sons
ISBN: 3527606416
Category : Science
Languages : en
Pages : 312
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Book Description
A new edition of this well-established monograph, this volume provides a comprehensive overview over the still fascinating field of chaos research. The authors include recent developments such as systems with restricted degrees of freedom but put also a strong emphasis on the mathematical foundations. Partly illustrated in color, this fourth edition features new sections from applied nonlinear science, like control of chaos, synchronisation of nonlinear systems, and turbulence, as well as recent theoretical concepts like strange nonchaotic attractors, on-off intermittency and spatio-temporal chaotic motion.
Author: Heinz Georg Schuster
Publisher: Jacaranda
ISBN:
Category : Science
Languages : en
Pages : 304
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Book Description
Author: Fabio Benatti
Publisher: Springer
ISBN: 9783540570172
Category : Science
Languages : en
Pages : 0
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Book Description
The purpose of this volume is to give a detailed account of a series of re sults concerning some ergodic questions of quantum mechanics which have the past six years following the formulation of a generalized been addressed in Kolmogorov-Sinai entropy by A.Connes, H.Narnhofer and W.Thirring. Classical ergodicity and mixing are fully developed topics of mathematical physics dealing with the lowest levels in a hierarchy of increasingly random behaviours with the so-called Bernoulli systems at its apex showing a structure that characterizes them as Kolmogorov (K-) systems. It seems not only reasonable, but also inevitable to use classical ergodic theory as a guide in the study of ergodic behaviours of quantum systems. The question is which kind of random behaviours quantum systems can exhibit and whether there is any way of classifying them. Asymptotic statistical independence and, correspondingly, complete lack of control over the distant future are typical features of classical K-systems. These properties are fully characterized by the dynamical entropy of Kolmogorov and Sinai, so that the introduction of a similar concept for quantum systems has provided the opportunity of raising meaningful questions and of proposing some non-trivial answers to them. Since in the following we shall be mainly concerned with infinite quantum systems, the algebraic approach to quantum theory will provide us with the necessary analytical tools which can be used in the commutative context, too.
Author: David Hobill
Publisher: Springer Science & Business Media
ISBN: 1475799934
Category : Science
Languages : en
Pages : 472
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Book Description
Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com plex nonlinear systems that cannot be broken down into the behavior of their con stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent.
Author: Jean-Pierre Gazeau
Publisher: IOS Press
ISBN: 1586037064
Category : Science
Languages : en
Pages : 349
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Book Description
Aims to reinforce the interface between physical sciences, theoretical computer science, and discrete mathematics. This book assembles theoretical physicists and specialists of theoretical informatics and discrete mathematics in order to learn about developments in cryptography, algorithmics, and more.
Author: Joseph L. McCauley
Publisher: Cambridge University Press
ISBN: 9780521467476
Category : Mathematics
Languages : en
Pages : 352
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Book Description
This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.
Author: Marisa Faggini
Publisher: Springer Science & Business Media
ISBN: 8847017785
Category : Mathematics
Languages : en
Pages : 252
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Book Description
In economics agents are assumed to choose on the basis of rational calculations aimed at the maximization of their pleasure or profit. Formally, agents are said to manifest transitive and consistent preferences in attempting to maximize their utility in the presence of several constraints. They operate according to the choice imperative: given a set of alternatives, choose the best. This imperative works well in a static and simplistic framework, but it may fail or vary when 'the best' is changing continuously. This approach has been questioned by a descriptive approach that springing from the complexity theory tries to give a scientific basis to the way in which individuals really choose, showing that those models of human nature is routinely falsified by experiments since people are neither selfish nor rational. Thus inductive rules of thumb are usually implemented in order to make decisions in the presence of incomplete and heterogeneous information sets.
Author: Gianfranco Minati
Publisher: World Scientific
ISBN: 981279347X
Category : Mathematics
Languages : en
Pages : 839
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Book Description
This book contains the Proceedings of the 2007 Conference of the Italian Systems Society. Papers deal with the interdisciplinary study of processes of emergence, considering theoretical aspects and applications from physics, cognitive science, biology, artificial intelligence, economics, architecture, philosophy, music and social systems. Such an interdisciplinary study implies the need to model and distinguish, in different disciplinary contexts, the establishment of structures, systems and systemic properties. Systems, as modeled by the observer, not only possess properties, but are also able to make emergent new properties. While current disciplinary models of emergence are based on theories of phase transitions, bifurcations, dissipative structures, multiple systems and organization, the present volume focuses on both generalizing those disciplinary models and identifying correspondences and new more general approaches. The general conceptual framework of the book relates to the attempt to build a general theory of emergence as a general theory of change, corresponding to Von Bertalanffy''s project for a general system theory.
Author: A. Selvam
Publisher: Luniver Press
ISBN: 1905986076
Category : Mathematics
Languages : en
Pages : 157
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Book Description
Atmosphere is a chaotic system. As such it is inherently unpredictable. The book applies chaos theory to understand and predict climate systems. Author presents a cell dynamical system model for turbulent fluid flows. The model envisages the irregular space-time fluctuations of the atmospheric flow pattern generated as a consequence of the superimposition of a continuum of eddies. The natural space-time variability is quantified in terms of the universal inverse power-law form of the statistical normal distribution. A range of possible applications of the cell dynamical system model for weather and climate system is discussed. The book provides a comprehensive reference material for scientists and academicians working in the field of atmospheric sciences and related topics.
Author: Anthony J Parsons
Publisher: CRC Press
ISBN: 0203498666
Category : Science
Languages : en
Pages : 437
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Book Description
Encompassing geomorphology, hydrology and agricultural engineering, this provides an interdisciplinary review of a topic important in both Scientific And Practical Terms - With The Specific Aim Of Promoting interaction between modellers, field workers and laboratory experimentalists.
