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Entropy in Dynamic Systems

2019-10-16 Science
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Release : 2019-10-16
Genre : Science
Kind : eBook
Book Rating : 163/5 ( reviews)

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Book Synopsis Entropy in Dynamic Systems by : Jan Awrejcewicz

Download or read book Entropy in Dynamic Systems written by Jan Awrejcewicz. This book was released on 2019-10-16. Available in PDF, EPUB and Kindle. Book excerpt: 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

2011-05-12 Mathematics
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Release : 2011-05-12
Genre : Mathematics
Kind : eBook
Book Rating : 872/5 ( reviews)

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Book Synopsis Entropy in Dynamical Systems by : Tomasz Downarowicz

Download or read book Entropy in Dynamical Systems written by Tomasz Downarowicz. This book was released on 2011-05-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamical Entropy in Operator Algebras

2006-09-22 Mathematics
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Release : 2006-09-22
Genre : Mathematics
Kind : eBook
Book Rating : 732/5 ( reviews)

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Book Synopsis Dynamical Entropy in Operator Algebras by : Sergey Neshveyev

Download or read book Dynamical Entropy in Operator Algebras written by Sergey Neshveyev. This book was released on 2006-09-22. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Entropy in Dynamic Systems

2019 Electronic books
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Release : 2019
Genre : Electronic books
Kind : eBook
Book Rating : 178/5 ( reviews)

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Book Synopsis Entropy in Dynamic Systems by : J. A. Tenreiro Machado

Download or read book Entropy in Dynamic Systems written by J. A. Tenreiro Machado. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topological Entropy and Equivalence of Dynamical Systems

1979 Ergodic theory
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Release : 1979
Genre : Ergodic theory
Kind : eBook
Book Rating : 195/5 ( reviews)

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Book Synopsis Topological Entropy and Equivalence of Dynamical Systems by : Roy L. Adler

Download or read book Topological Entropy and Equivalence of Dynamical Systems written by Roy L. Adler. This book was released on 1979. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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