An invariant for continuous mappings
J. S. Chawla (1980)
Kybernetika
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J. S. Chawla (1980)
Kybernetika
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Riečan, B.
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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...
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...
François Blanchard (1993)
Bulletin de la Société Mathématique de France
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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.
Gselmann, Eszter (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Chakrabarti, C.G., Chakrabarty, Indranil (2005)
International Journal of Mathematics and Mathematical Sciences
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Coven, E.M., Smítal, J. (1993)
Acta Mathematica Universitatis Comenianae. New Series
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Kyewon Koh Park, Uijung Lee (2004)
Studia Mathematica
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Topological and metric entropy pairs of ℤ²-actions are defined and their properties are investigated, analogously to ℤ-actions. In particular, mixing properties are studied in connection with entropy pairs.