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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.

Topological Entropy and Equivalence of Dynamical Systems

1979 Ergodic theory
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Release : 1979
Genre : Ergodic theory
Kind : eBook
Book Rating : 180/5 ( reviews)

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Book Synopsis Topological Entropy and Equivalence of Dynamical Systems by : American Mathematical Society

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

Combinatorial Dynamics And Entropy In Dimension One

1993-06-04 Mathematics
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Release : 1993-06-04
Genre : Mathematics
Kind : eBook
Book Rating : 220/5 ( reviews)

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Book Synopsis Combinatorial Dynamics And Entropy In Dimension One by : Alseda Luis

Download or read book Combinatorial Dynamics And Entropy In Dimension One written by Alseda Luis. This book was released on 1993-06-04. Available in PDF, EPUB and Kindle. Book excerpt: 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

Invariance Entropy for Deterministic Control Systems

2013-10-02 Mathematics
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Release : 2013-10-02
Genre : Mathematics
Kind : eBook
Book Rating : 886/5 ( reviews)

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Book Synopsis Invariance Entropy for Deterministic Control Systems by : Christoph Kawan

Download or read book Invariance Entropy for Deterministic Control Systems written by Christoph Kawan. This book was released on 2013-10-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ergodic Theory and Topological Dynamics

1976-11-15 Mathematics
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Release : 1976-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 863/5 ( reviews)

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Book Synopsis Ergodic Theory and Topological Dynamics by :

Download or read book Ergodic Theory and Topological Dynamics written by . This book was released on 1976-11-15. Available in PDF, EPUB and Kindle. Book excerpt: Ergodic Theory and Topological Dynamics

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