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

top
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

top

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

top
  1. Adler K.A, Kohnheim A., McAndrew M., Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319. (1965) MR0175106
  2. Bowen R., Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414. (1971) Zbl0212.29201MR0274707
  3. Bowen R., Topological entropy for noncompact sets, Trans. Amer. Math. Soc. 184 (1973), 125-156. (1973) MR0338317
  4. Frolík Z., A characterization of topologically complete spaces in the sense of E. Čech in terms of convergence of functions, Czechoslovak Math. J. 13 (88) (1962), 148-151. (1962) MR0155290
  5. Herrlich H., Topological structures, Proc. Sympos. in honour of J. de Groot, pp. 59-122, Math. Centre Tracts, no. 52, Math. Centrum, Amsterdam, 1974. Zbl0589.54018MR0358706
  6. Herrlich H., Categorical topology 1971-1981, Proc. Fifth Prague Topological Sympos. 1981, pp. 279-383; Heldermann, Berlin, 1982. Zbl0502.54001MR0698425
  7. Katětov M., Spaces defined by giving a family of centered systems (in Russian), Uspehi Mat. Nauk 31 (1976), no. 5 (191), 95-107 Russian Math. Surveys 31, (1976), 111-123. (1976) MR0448278
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.