Entropy of piecewise monotone mappings

M. Misiurewicz; W. Szlenk

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Forti, G.L., Paganoni, L. (1998)

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Coven, E.M., Smítal, J. (1993)

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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?

Entropies of self-mappings of topological spaces with richer structures

Miroslav Katětov (1993)

Commentationes Mathematicae Universitatis Carolinae

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For mappings $f : S \to S$ , where $S$ is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the $δ$ -entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the $δ$ -entropy. Some connections with other characteristics of self-mappings are considered. We also introduce and examine an entropy for subsets of $S^{N}$ , which is closely connected with the $δ$ -entropy of $f : S \to S$ .

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Riečan, B.

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