# Entropies of self-mappings of topological spaces with richer structures

Commentationes Mathematicae Universitatis Carolinae (1993)

- Volume: 34, Issue: 4, page 747-768
- ISSN: 0010-2628

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topKatětov, Miroslav. "Entropies of self-mappings of topological spaces with richer structures." Commentationes Mathematicae Universitatis Carolinae 34.4 (1993): 747-768. <http://eudml.org/doc/247480>.

@article{Katětov1993,

abstract = {For mappings $f\,:\, S\rightarrow S$, where $S$ is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the $\delta $-entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the $\delta $-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 $\delta $-entropy of $f\,:\, S\rightarrow S$.},

author = {Katětov, Miroslav},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {entropy; merotopic space; self-mapping; diameter function; merotopic space; diameter function; topological entropy; entropy of self-mappings},

language = {eng},

number = {4},

pages = {747-768},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Entropies of self-mappings of topological spaces with richer structures},

url = {http://eudml.org/doc/247480},

volume = {34},

year = {1993},

}

TY - JOUR

AU - Katětov, Miroslav

TI - Entropies of self-mappings of topological spaces with richer structures

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1993

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 34

IS - 4

SP - 747

EP - 768

AB - For mappings $f\,:\, S\rightarrow S$, where $S$ is a merotopic space equipped with a diameter function, we introduce and examine an entropy, called the $\delta $-entropy. The topological entropy and the entropy of self-mappings of metric spaces are shown to be special cases of the $\delta $-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 $\delta $-entropy of $f\,:\, S\rightarrow S$.

LA - eng

KW - entropy; merotopic space; self-mapping; diameter function; merotopic space; diameter function; topological entropy; entropy of self-mappings

UR - http://eudml.org/doc/247480

ER -

## References

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