Entropies of self-mappings of topological spaces with richer structures

Miroslav Katětov

Commentationes Mathematicae Universitatis Carolinae (1993)

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

Abstract

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For mappings f : S → 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 → S .

How to cite

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Katětov, 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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  8. Katětov M., On entropy-like functionals and codes for metrized probability spaces I, Comment. Math. Univ. Carolinae 31 (1990), 49-66. (1990) MR1056171
  9. Katětov M., On entropy-like functionals and codes for metrized probability spaces II, Comment. Math. Univ. Carolinae 33 (1992), 79-95. (1992) MR1173750
  10. Katětov M., Entropy-like functionals: conceptual background and some results, Comment. Math. Univ. Carolinae 33 (1992), 645-660. (1992) MR1240186

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