Entropy In Dynamic Systems

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Entropy in Dynamic Systems

Jan Awrejcewicz,J. A. Tenreiro Machado
Entropy in Dynamic Systems Book PDF

Author : Jan Awrejcewicz,J. A. Tenreiro Machado
Publisher : MDPI
Page : 172 pages
File Size : 48,7 Mb
Release : 2019-10-16
Category : Science
ISBN : 9783039216161

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Entropy in Dynamic Systems by Jan Awrejcewicz,J. A. Tenreiro Machado Pdf

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.

Dynamical Entropy in Operator Algebras

Sergey Neshveyev,Erling Størmer
Dynamical Entropy in Operator Algebras Book PDF

Author : Sergey Neshveyev,Erling Størmer
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 41,6 Mb
Release : 2006-09-22
Category : Mathematics
ISBN : 9783540346739

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Dynamical Entropy in Operator Algebras by Sergey Neshveyev,Erling Størmer Pdf

The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. It is the only monograph on this topic. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.

Topological Entropy and Equivalence of Dynamical Systems

Roy L. Adler,Brian Marcus
Topological Entropy and Equivalence of Dynamical Systems Book PDF

Author : Roy L. Adler,Brian Marcus
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 55,6 Mb
Release : 1979
Category : Ergodic theory
ISBN : 9780821822197

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Topological Entropy and Equivalence of Dynamical Systems by Roy L. Adler,Brian Marcus Pdf

The purpose of this work is to prove a theorem for topological entropy analogous to Ornstein's result for measure entropy. For this a natural class of dynamical systems is needed to play the same role for topological entropy as the Bernoulli shifts do for measure entropy. Fortunately there is just such a class--the topological Markov shifts. The main result of this paper is that topological entropy along with another number, called the ergodic period, is a complete set of invariants under this new equivalence relation for the class of topological Markov shifts.

Combinatorial Dynamics And Entropy In Dimension One

Alseda Luis,Llibre Jaume,Misiurewicz Michal
Combinatorial Dynamics And Entropy In Dimension One Book PDF

Author : Alseda Luis,Llibre Jaume,Misiurewicz Michal
Publisher : World Scientific Publishing Company
Page : 344 pages
File Size : 48,5 Mb
Release : 1993-06-04
Category : Mathematics
ISBN : 9789814553223

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Combinatorial Dynamics And Entropy In Dimension One by Alseda Luis,Llibre Jaume,Misiurewicz Michal Pdf

In last thirty years an explosion of interest in the study of nonlinear dynamical systems occured. The theory of one-dimensional dynamical systems has grown out in many directions. One of them has its roots in the Sharkovski0 Theorem. This beautiful theorem describes the possible sets of periods of all cycles of maps of an interval into itself. Another direction has its main objective in measuring the complexity of a system, or the amount of chaos present in it. A good way of doing this is to compute topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. Many comments are added referring to related problems, and historical remarks are made. Request Inspection Copy

Entropy in Dynamic Systems

J. A. Tenreiro Machado,Jan Awrejcewicz
Entropy in Dynamic Systems Book PDF

Author : J. A. Tenreiro Machado,Jan Awrejcewicz
Publisher : Unknown
Page : 1 pages
File Size : 46,6 Mb
Release : 2019
Category : Electronic books
ISBN : 3039216171

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Entropy in Dynamic Systems by J. A. Tenreiro Machado,Jan Awrejcewicz Pdf

In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.

Entropy in Dynamical Systems

Tomasz Downarowicz
Entropy in Dynamical Systems Book PDF

Author : Tomasz Downarowicz
Publisher : Cambridge University Press
Page : 405 pages
File Size : 47,6 Mb
Release : 2011-05-12
Category : Mathematics
ISBN : 9781139500876

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Entropy in Dynamical Systems by Tomasz Downarowicz Pdf

This comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the Ornstein–Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors

Christos Volos,Sajad Jafari,Jacques Kengne,Jesus M. Munoz-Pacheco,Karthikeyan Rajagopal
Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self excited Attractors Book PDF

Author : Christos Volos,Sajad Jafari,Jacques Kengne,Jesus M. Munoz-Pacheco,Karthikeyan Rajagopal
Publisher : MDPI
Page : 290 pages
File Size : 41,5 Mb
Release : 2019-05-03
Category : Technology & Engineering
ISBN : 9783038978985

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Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors by Christos Volos,Sajad Jafari,Jacques Kengne,Jesus M. Munoz-Pacheco,Karthikeyan Rajagopal Pdf

In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.

Local Entropy Theory of a Random Dynamical System

Anthony H. Dooley, Guohua Zhang
Local Entropy Theory of a Random Dynamical System Book PDF

Author : Anthony H. Dooley, Guohua Zhang
Publisher : American Mathematical Soc.
Page : 106 pages
File Size : 53,6 Mb
Release : 2014-12-20
Category : Mathematics
ISBN : 9781470410551

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Local Entropy Theory of a Random Dynamical System by Anthony H. Dooley, Guohua Zhang Pdf

In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.

Invariance Entropy for Deterministic Control Systems

Christoph Kawan
Invariance Entropy for Deterministic Control Systems Book PDF

Author : Christoph Kawan
Publisher : Springer
Page : 290 pages
File Size : 52,7 Mb
Release : 2013-10-02
Category : Mathematics
ISBN : 9783319012889

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Invariance Entropy for Deterministic Control Systems by Christoph Kawan Pdf

This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.

Combinatorial Dynamics and Entropy in Dimension One

Ll Alsedà,Jaume Llibre,Michał Misiurewicz
Combinatorial Dynamics and Entropy in Dimension One Book PDF

Author : Ll Alsedà,Jaume Llibre,Michał Misiurewicz
Publisher : World Scientific Publishing Company Incorporated
Page : 415 pages
File Size : 53,6 Mb
Release : 2000
Category : Mathematics
ISBN : 9810240538

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Combinatorial Dynamics and Entropy in Dimension One by Ll Alsedà,Jaume Llibre,Michał Misiurewicz Pdf

This book introduces the reader to two of the main directions of one-dimensional dynamics. The first has its roots in the Sharkovskii theorem, which describes the possible sets of periods of all periodic orbits of a continuous map of an interval into itself. The whole theory, which was developed based on this theorem, deals mainly with combinatorial objects, permutations, graphs, etc.: it is called combinatorial dynamics. The second direction has its main objective in measuring the complexity of a system, or the degree of "chaos" present in it. A good way of doing this is to study the topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. The second edition contains two new appendices, where an extension of the theory to tree and graph maps is presented without technical proofs.

Permutation Complexity in Dynamical Systems

José Amigó
Permutation Complexity in Dynamical Systems Book PDF

Author : José Amigó
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 50,6 Mb
Release : 2010-03-20
Category : Science
ISBN : 9783642040849

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Permutation Complexity in Dynamical Systems by José Amigó Pdf

The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.

Entropy of Complex Processes and Systems

Eugene Barsky
Entropy of Complex Processes and Systems Book PDF

Author : Eugene Barsky
Publisher : Elsevier
Page : 308 pages
File Size : 51,5 Mb
Release : 2020-08-17
Category : Science
ISBN : 9780128216620

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Entropy of Complex Processes and Systems by Eugene Barsky Pdf

Entropy of Complex Processes and Systems formalizes our understanding of many complex processes, including the development of the methodology of analytical computation of complex processes as applied in many industries, such as ore processing, or more generally, in areas of natural sciences. The adequacy of the results of these calculations is confirmed by numerous experimental data obtained both on pilots and industrial facilities. The book also provides a thorough analysis of the underlying physical foundations of entropy performed from new standpoints that are of interest to theoreticians studying contemporary expositions. Provides methodologies for controlling and optimizing complex processes in branches of industry that involve transformation of materials or substances Describes entropy as the universal characteristic of a stochastic process independent of the system Introduces a new definition of entropy specifically related to dynamical phenomena

Entropy

Andreas Greven,Gerhard Keller,Gerald Warnecke
Entropy Book PDF

Author : Andreas Greven,Gerhard Keller,Gerald Warnecke
Publisher : Princeton University Press
Page : 376 pages
File Size : 43,9 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400865222

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Entropy by Andreas Greven,Gerhard Keller,Gerald Warnecke Pdf

The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding.

Dynamical Systems

Jürgen Jost
Dynamical Systems Book PDF

Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 199 pages
File Size : 40,7 Mb
Release : 2005-11-24
Category : Science
ISBN : 9783540288893

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Dynamical Systems by Jürgen Jost Pdf

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

Smooth Ergodic Theory of Random Dynamical Systems

Pei-Dong Liu,Min Qian
Smooth Ergodic Theory of Random Dynamical Systems Book PDF

Author : Pei-Dong Liu,Min Qian
Publisher : Springer
Page : 233 pages
File Size : 50,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540492917

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Smooth Ergodic Theory of Random Dynamical Systems by Pei-Dong Liu,Min Qian Pdf

This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.