| Title:
|
Equidistribution in the dual group of the $S$-adic integers (English) |
| Author:
|
Urban, Roman |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
4 |
| Year:
|
2014 |
| Pages:
|
911-931 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be the quotient group of the $S$-adele ring of an algebraic number field by the discrete group of $S$-integers. Given a probability measure $\mu $ on $X^d$ and an endomorphism $T$ of $X^d$, we consider the relation between uniform distribution of the sequence $T^n\bold {x}$ for $\mu $-almost all $\bold {x}\in X^d$ and the behavior of $\mu $ relative to the translations by some rational subgroups of $X^d$. The main result of this note is an extension of the corresponding result for the $d$-dimensional torus $\mathbb T^d$ due to B. Host. (English) |
| Keyword:
|
uniform distribution modulo $1$ |
| Keyword:
|
equidistribution in probability |
| Keyword:
|
algebraic number fields |
| Keyword:
|
$S$-adele ring |
| Keyword:
|
$S$-integer dynamical system |
| Keyword:
|
algebraic dynamics |
| Keyword:
|
topological dynamics |
| Keyword:
|
$a$-adic solenoid |
| MSC:
|
11J71 |
| MSC:
|
11K06 |
| MSC:
|
54H20 |
| idZBL:
|
Zbl 06433704 |
| idMR:
|
MR3304788 |
| DOI:
|
10.1007/s10587-014-0143-4 |
| . |
| Date available:
|
2015-02-09T17:25:50Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144151 |
| . |
| Reference:
|
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| . |
