| Title:
|
Topological sequence entropy for maps of the circle (English) |
| Author:
|
Hric, Roman |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
53-59 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A continuous map $f$ of the interval is chaotic iff there is an increasing sequence of nonnegative integers $T$ such that the topological sequence entropy of $f$ relative to $T$, $h_T(f)$, is positive ([FS]). On the other hand, for any increasing sequence of nonnegative integers $T$ there is a chaotic map $f$ of the interval such that $h_T(f)=0$ ([H]). We prove that the same results hold for maps of the circle. We also prove some preliminary results concerning topological sequence entropy for maps of general compact metric spaces. (English) |
| Keyword:
|
chaotic map |
| Keyword:
|
circle map |
| Keyword:
|
topological sequence entropy |
| MSC:
|
26A18 |
| MSC:
|
37B40 |
| MSC:
|
37D45 |
| MSC:
|
37E10 |
| MSC:
|
54H20 |
| MSC:
|
58F13 |
| idZBL:
|
Zbl 1039.37007 |
| idMR:
|
MR1756926 |
| . |
| Date available:
|
2009-01-08T18:58:22Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119140 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| . |
