| Title:
|
On self-similar subgroups in the sense of IFS (English) |
| Author:
|
Saltan, Mustafa |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
26 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
1-10 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we first give several properties with respect to subgroups of self-similar groups in the sense of iterated function system (IFS). We then prove that some subgroups of $p$-adic numbers $\mathbb{Q}_{p}$ are strong self-similar in the sense of IFS. (English) |
| Keyword:
|
Self-similar group |
| Keyword:
|
Cantor set |
| Keyword:
|
$p$-adic integers. |
| MSC:
|
11E95 |
| MSC:
|
28A80 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 06996469 |
| idMR:
|
MR3827139 |
| . |
| Date available:
|
2018-11-06T16:16:47Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147451 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Falconer, K. J.: Fractal Geometry.2003, Mathematical Foundations and Application, John Wiley, MR 2118797 |
| Reference:
|
[4] Gouvêa, F. Q.: $p$-adic Numbers.1997, Springer-Verlag, Berlin, MR 1488696 |
| Reference:
|
[5] Hutchinson, J. E.: Fractals and self-similarity.Indiana Univ. Math. J., 30, 5, 1981, 713-747, Zbl 0598.28011, MR 0625600, 10.1512/iumj.1981.30.30055 |
| Reference:
|
[6] Mandelbrot, B. B.: The Fractal Geometry of Nature.1983, W. H. Freeman and Company, New York, MR 0665254 |
| Reference:
|
[7] Robert, A. M.: A Course in $p$-adic Analysis.2000, Springer, Zbl 0947.11035, MR 1760253 |
| Reference:
|
[8] Saltan, M., Demir, B.: Self-similar groups in the sense of an IFS and their properties.J. Math. Anal. Appl., 408, 2, 2013, 694-704, MR 3085063, 10.1016/j.jmaa.2013.06.040 |
| Reference:
|
[9] Saltan, M., Demir, B.: An iterated function system for the closure of the adding machine group.Fractals, 23, 3, 2015, DOI: 10.1142/S0218348X15500334. MR 3375691, 10.1142/S0218348X15500334 |
| Reference:
|
[10] Schikhof, W. H.: Ultrametric Calculus an Introduction to $p$-adic Calculus.1984, Cambridge University Press, New York, MR 0791759 |
| . |
