On self-similar subgroups in the sense of IFS

Mustafa Saltan

Communications in Mathematics (2018)

  • Volume: 26, Issue: 1, page 1-10
  • ISSN: 1804-1388

Abstract

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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 ℚ p are strong self-similar in the sense of IFS.

How to cite

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Saltan, Mustafa. "On self-similar subgroups in the sense of IFS." Communications in Mathematics 26.1 (2018): 1-10. <http://eudml.org/doc/294298>.

@article{Saltan2018,
abstract = {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.},
author = {Saltan, Mustafa},
journal = {Communications in Mathematics},
keywords = {Self-similar group; Cantor set; $p$-adic integers},
language = {eng},
number = {1},
pages = {1-10},
publisher = {University of Ostrava},
title = {On self-similar subgroups in the sense of IFS},
url = {http://eudml.org/doc/294298},
volume = {26},
year = {2018},
}

TY - JOUR
AU - Saltan, Mustafa
TI - On self-similar subgroups in the sense of IFS
JO - Communications in Mathematics
PY - 2018
PB - University of Ostrava
VL - 26
IS - 1
SP - 1
EP - 10
AB - 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.
LA - eng
KW - Self-similar group; Cantor set; $p$-adic integers
UR - http://eudml.org/doc/294298
ER -

References

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  1. Barnsley, M. F., Fractals Everywhere, 1988, Academic Press, Boston, (1988) MR0977274
  2. Demir, B., Saltan, M., A self-similar group in the sense of iterated function system, Far East J. Math. Sci., 60, 1, 2012, 83-99, (2012) MR2953920
  3. Falconer, K. J., Fractal Geometry, 2003, Mathematical Foundations and Application, John Wiley, (2003) MR2118797
  4. Gouvêa, F. Q., p -adic Numbers, 1997, Springer-Verlag, Berlin, (1997) MR1488696
  5. Hutchinson, J. E., 10.1512/iumj.1981.30.30055, Indiana Univ. Math. J., 30, 5, 1981, 713-747, (1981) Zbl0598.28011MR0625600DOI10.1512/iumj.1981.30.30055
  6. Mandelbrot, B. B., The Fractal Geometry of Nature, 1983, W. H. Freeman and Company, New York, (1983) MR0665254
  7. Robert, A. M., A Course in p -adic Analysis, 2000, Springer, (2000) Zbl0947.11035MR1760253
  8. Saltan, M., Demir, B., 10.1016/j.jmaa.2013.06.040, J. Math. Anal. Appl., 408, 2, 2013, 694-704, (2013) MR3085063DOI10.1016/j.jmaa.2013.06.040
  9. Saltan, M., Demir, B., 10.1142/S0218348X15500334, Fractals, 23, 3, 2015, DOI: 10.1142/S0218348X15500334. (2015) MR3375691DOI10.1142/S0218348X15500334
  10. Schikhof, W. H., Ultrametric Calculus an Introduction to p -adic Calculus, 1984, Cambridge University Press, New York, (1984) MR0791759

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