Comparing measure theoretic entropy for -finite measures with topological entropy
Magda Komorníková, Jozef Komorník (1983)
Mathematica Slovaca
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Magda Komorníková, Jozef Komorník (1983)
Mathematica Slovaca
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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...
Michał Misiurewicz (1976)
Studia Mathematica
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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...
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.
Riečan, B.
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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?
Magda Komorníková, Jozef Komorník (1983)
Mathematica Slovaca
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Dikran Dikranjan, Hans-Peter A. Kunzi (2015)
Topological Algebra and its Applications
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We discuss the connection between the topological entropy and the uniform entropy and answer several open questions from [10, 15]. We also correct several erroneous statements given in [10, 18] without proof.
Koichi Yano (1980)
Inventiones mathematicae
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Young-Ho Ahn, Dou Dou, Kyewon Koh Park (2010)
Studia Mathematica
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Recently the notions of entropy dimension for topological and measurable dynamical systems were introduced in order to study the complexity of zero entropy systems. We exhibit a class of strictly ergodic models whose topological entropy dimensions range from zero to one and whose measure-theoretic entropy dimensions are identically zero. Hence entropy dimension does not obey the variational principle.