A remark on positive topological entropy of -buffer switched flow networks.
Yang, Xiao-Song (2005)
Discrete Dynamics in Nature and Society
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Yang, Xiao-Song (2005)
Discrete Dynamics in Nature and Society
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Francisco Balibrea (2015)
Topological Algebra and its Applications
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Discrete dynamical systems are given by the pair (X, f ) where X is a compact metric space and f : X → X a continuous maps. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. Among them, one of the most popular is that of topological entropy. In modern applications other conditions on X and f have been considered. For example X can be non-compact or f can be discontinuous (only in a finite number of points and with bounded...
Cánovas, Jose S., Medina, David López (2010)
Discrete Dynamics in Nature and Society
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Forti, G.L., Paganoni, L. (1998)
Mathematica Pannonica
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Riečan, B.
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Louis Block, Ethan M. Coven (1989)
Banach Center Publications
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François Blanchard (1993)
Bulletin de la Société Mathématique de France
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Dawid Huczek (2012)
Colloquium Mathematicae
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We prove that an invertible zero-dimensional dynamical system has an invariant measure of maximal entropy if and only if it is an extension of an asymptotically h-expansive system of equal topological entropy.
Tomasz Downarowicz, Jacek Serafin (2002)
Fundamenta Mathematicae
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We consider a pair of topological dynamical systems on compact Hausdorff (not necessarily metrizable) spaces, one being a factor of the other. Measure-theoretic and topological notions of fiber entropy and conditional entropy are defined and studied. Abramov and Rokhlin's definition of fiber entropy is extended, using disintegration. We prove three variational principles of conditional nature, partly generalizing some results known before in metric spaces: (1) the topological conditional...
Jozef Bobok (2002)
Studia Mathematica
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We answer affirmatively Coven's question [PC]: Suppose f: I → I is a continuous function of the interval such that every point has at least two preimages. Is it true that the topological entropy of f is greater than or equal to log 2?
Michał Misiurewicz (1976)
Studia Mathematica
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Canovas, J.S. (1999)
Acta Mathematica Universitatis Comenianae. New Series
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Christoph Kawan (2014)
Nonautonomous Dynamical Systems
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We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn, μn) of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1. This notion generalizes the classical concept of metric entropy established by Kolmogorov and Sinai, and is related via a variational inequality to the topological entropy of nonautonomous systems as defined by Kolyada, Misiurewicz, and Snoha. Moreover, it shares several properties with the...
Coven, E.M., Smítal, J. (1993)
Acta Mathematica Universitatis Comenianae. New Series
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