A disjointness theorem involving topological entropy
François Blanchard (1993)
Bulletin de la Société Mathématique de France
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Displaying similar documents to “An invariant for continuous mappings”
A disjointness theorem involving topological entropy
On topological entropy
Riečan, B.
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Entropy-minimality.
Coven, E.M., Smítal, J. (1993)
Acta Mathematica Universitatis Comenianae. New Series
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Fiber entropy and conditional variational principles in compact non-metrizable spaces
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...
On the origin and development of some notions of entropy
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...
Entropies of self-mappings of topological spaces with richer structures
Miroslav Katětov (1993)
Commentationes Mathematicae Universitatis Carolinae
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For mappings , where is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the -entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the -entropy. Some connections with other characteristics of self-mappings are considered. We also introduce and examine an entropy for subsets of , which is closely connected with the -entropy of .
Uniform entropy vs topological entropy
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.