A distributionally chaotic triangular map with zero sequence topological entropy.
Forti, G.L., Paganoni, L. (1998)
Mathematica Pannonica
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Forti, G.L., Paganoni, L. (1998)
Mathematica Pannonica
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Cánovas, Jose S., Medina, David López (2010)
Discrete Dynamics in Nature and Society
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Rafał Pikuła (2007)
Colloquium Mathematicae
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We compare four different notions of chaos in zero-dimensional systems (subshifts). We provide examples showing that in that case positive topological entropy does not imply strong chaos, strong chaos does not imply complicated dynamics at all, and ω-chaos does not imply Li-Yorke chaos.
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...
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?
Yang, Xiao-Song, Bai, Xiaoming (2006)
Discrete Dynamics in Nature and Society
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Michał Misiurewicz (1976)
Studia Mathematica
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Louis Block, Ethan M. Coven (1989)
Banach Center Publications
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Sylvie Ruette (2005)
Studia Mathematica
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We prove that for continuous interval maps the existence of a non-empty closed invariant subset which is transitive and sensitive to initial conditions is implied by positive topological entropy and implies chaos in the sense of Li-Yorke, and we exhibit examples showing that these three notions are distinct.
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.
Cánovas, J.S. (2003)
Mathematica Pannonica
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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...
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.
Günther Palm (1975)
Publications mathématiques et informatique de Rennes
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Koichi Yano (1980)
Inventiones mathematicae
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