| Title:
|
On the fixed points in an $\omega$-limit set (English) |
| Author:
|
Ceder, J. G. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
117 |
| Issue:
|
4 |
| Year:
|
1992 |
| Pages:
|
349-364 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $M$ and $K$ be closed subsets of [0,1] with $K$ a subset of the limit points of $M$. Necessary and sufficient conditions are found for the existence of a continuous function $f:[0,1]\rightarrow [0,1]$ such that $M$ is an $\omega$-limit set for $f$ and $K$ is the set of fixed points of $f$ in $M$. (English) |
| Keyword:
|
$\omega$-limit set |
| Keyword:
|
fixed points |
| MSC:
|
26A18 |
| MSC:
|
54C30 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 0772.26005 |
| idMR:
|
MR1197285 |
| DOI:
|
10.21136/MB.1992.126065 |
| . |
| Date available:
|
2009-09-24T20:54:51Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126065 |
| . |
| 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 (1989-90), 483-510. MR 1059418, 10.2307/44152033 |
| Reference:
|
[2] A. M. Bruckner J. Smítal: The structure of $\omega$-limit sets for continuous maps of an interval.to appear in Časopis pro Pěstování Mat. MR 1154053 |
| Reference:
|
[3] M. J. Evans P. D. Humke C. M. Lee, R. J. O'Malley: Characterizations of turbulent one-dimensional mappings via $\omega$-limit sets.to appear. |
| . |
