| Title:
|
The structure of $\omega$-limit sets for continuous maps of the interval (English) |
| Author:
|
Bruckner, Andrew M. |
| Author:
|
Smítal, Jaroslav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
117 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
42-47 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that every infinite nowhere dense compact subset of the interval $I$ is an $\omega$-limit set of homoclinic type for a continuous function from $I$ to $I$. (English) |
| Keyword:
|
discrete dynamical system |
| Keyword:
|
continuous map |
| Keyword:
|
$\omega$-limit set |
| Keyword:
|
homoclinic set |
| MSC:
|
26A18 |
| MSC:
|
37C70 |
| MSC:
|
54H20 |
| MSC:
|
58F12 |
| idZBL:
|
Zbl 0762.26003 |
| idMR:
|
MR1154053 |
| DOI:
|
10.21136/MB.1992.126240 |
| . |
| Date available:
|
2009-09-24T20:49:39Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126240 |
| . |
| Reference:
|
[1] S. J. Agronsky A. M. Bruckner J. G. Ceder T. L. Pearson: The structure of $\omega$-limit sets for continuous functions.Real Analysis Exchange 15 (1989-1990), 483-510. MR 1059418, 10.2307/44152033 |
| Reference:
|
[2] A. N. Šarkovskii: Attracting and attracted sets.Soviet Math. Dokl. 6 (1965), 268-270. |
| Reference:
|
[3] A. N. Šarkovskii: The partially ordered system of attracting sets.Soviet Math. Dokl. 7 (1966), 1384-1386. MR 0209413 |
| Reference:
|
[4] A. N. Šarkovskii: Attracting sets containing no cycles.Ukrain. Mat. Ž. 20 (1968), 136-142. (In Russian.) MR 0225314 |
| . |
