| Title:
|
The structure of disjoint iteration groups on the circle (English) |
| Author:
|
Ciepliński, Krzysztof |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
131-153 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The aim of the paper is to investigate the structure of disjoint iteration groups on the unit circle ${\mathbb{S}^1}$, that is, families ${\mathcal F}=\lbrace F^{v}\:{\mathbb{S}^1}\longrightarrow {\mathbb{S}^1}\; v\in V\rbrace $ of homeomorphisms such that \[ F^{v_{1}}\circ F^{v_{2}}=F^{v_{1}+v_{2}},\quad v_1, v_2\in V, \] and each $F^{v}$ either is the identity mapping or has no fixed point ($(V, +)$ is an arbitrary $2$-divisible nontrivial (i.e., $\mathop {\mathrm card}V>1$) abelian group). (English) |
| Keyword:
|
(disjoint |
| Keyword:
|
non-singular |
| Keyword:
|
singular |
| Keyword:
|
non-dense |
| Keyword:
|
dense |
| Keyword:
|
discrete) iteration group |
| Keyword:
|
degree |
| Keyword:
|
periodic point |
| Keyword:
|
orientation-preserving homeomorphism |
| Keyword:
|
rotation number |
| Keyword:
|
limit set |
| Keyword:
|
orbit |
| Keyword:
|
system of functional equations |
| MSC:
|
20F28 |
| MSC:
|
20F38 |
| MSC:
|
30D05 |
| MSC:
|
37B99 |
| MSC:
|
37E10 |
| MSC:
|
37E45 |
| MSC:
|
39B12 |
| MSC:
|
39B32 |
| MSC:
|
39B72 |
| idZBL:
|
Zbl 1047.37024 |
| idMR:
|
MR2040226 |
| . |
| Date available:
|
2009-09-24T11:10:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127871 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
