| Title:
|
The Banach contraction mapping principle and cohomology (English) |
| Author:
|
Janoš, Ludvík |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
605-610 |
| . |
| Category:
|
math |
| . |
| Summary:
|
By a dynamical system $(X,T)$ we mean the action of the semigroup $(\Bbb Z^+,+)$ on a metrizable topological space $X$ induced by a continuous selfmap $T:X\rightarrow X$. Let $M(X)$ denote the set of all compatible metrics on the space $X$. Our main objective is to show that a selfmap $T$ of a compact space $X$ is a Banach contraction relative to some $d_1\in M(X)$ if and only if there exists some $d_2\in M(X)$ which, regarded as a $1$-cocycle of the system $(X,T)\times (X,T)$, is a coboundary. (English) |
| Keyword:
|
$B$-system |
| Keyword:
|
$E$-system |
| MSC:
|
37B25 |
| MSC:
|
37B99 |
| MSC:
|
47H10 |
| MSC:
|
54H15 |
| MSC:
|
54H20 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1087.37502 |
| idMR:
|
MR1795089 |
| . |
| Date available:
|
2009-01-08T19:05:33Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119193 |
| . |
| 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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| Reference:
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| . |
