| Title:
|
Entropies of self-mappings of topological spaces with richer structures (English) |
| Author:
|
Katětov, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
747-768 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $f\,:\, S\rightarrow S$. (English) |
| Keyword:
|
entropy |
| Keyword:
|
merotopic space |
| Keyword:
|
self-mapping |
| Keyword:
|
diameter function |
| MSC:
|
54C70 |
| MSC:
|
54E17 |
| idZBL:
|
Zbl 0839.54022 |
| idMR:
|
MR1263803 |
| . |
| Date available:
|
2009-01-08T18:08:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118631 |
| . |
| Reference:
|
[AKM65] Adler K.A, Kohnheim A., McAndrew M.: Topological entropy.Trans. Amer. Math. Soc. 114 (1965), 309-319. MR 0175106 |
| Reference:
|
[B71] Bowen R.: Entropy for group endomorphisms and homogeneous spaces.Trans. Amer. Math. Soc. 153 (1971), 401-414. Zbl 0212.29201, MR 0274707 |
| Reference:
|
[B73] Bowen R.: Topological entropy for noncompact sets.Trans. Amer. Math. Soc. 184 (1973), 125-156. MR 0338317 |
| Reference:
|
[F62] 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. MR 0155290 |
| Reference:
|
[H74] Herrlich H.: Topological structures.Proc. Sympos. in honour of J. de Groot, pp. 59-122, Math. Centre Tracts, no. 52, Math. Centrum, Amsterdam, 1974. Zbl 0589.54018, MR 0358706 |
| Reference:
|
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| Reference:
|
[K76] 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. MR 0448278 |
| Reference:
|
[K90] Katětov M.: On entropy-like functionals and codes for metrized probability spaces I.Comment. Math. Univ. Carolinae 31 (1990), 49-66. MR 1056171 |
| Reference:
|
[K92a] Katětov M.: On entropy-like functionals and codes for metrized probability spaces II.Comment. Math. Univ. Carolinae 33 (1992), 79-95. MR 1173750 |
| Reference:
|
[K92b] Katětov M.: Entropy-like functionals: conceptual background and some results.Comment. Math. Univ. Carolinae 33 (1992), 645-660. MR 1240186 |
| . |
