Year 2016,
Volume: 4 Issue: 2, 113 - 120, 03.10.2016
Abstract
Bir köklü ağaç otomorfizminin kendine benzerlik kavramı (Sidki, 1998; Nekrashevych, 2005) de verilmektedir. (Saltan ve Demir, 2013) de, yinelemeli fonksiyon sistemi (YFS) anlamında kendine benzer gruplarlar tanımlanmakta ve bu grupların özellikleri ayrıntılı olarak incelenmektedir. Bu çalışmada, YFS anlamında kendine benzer grup ve ağaç otomorfizminin kendine benzerlik kavramlarının birbirlerini gerektirmediği gösterilmektedir. Ayrıca bu iki tanımın bazı benzer ve farklı tarafları araştırılmaktadır.
References
- Mandelbrot BB. The Fractal Geometry of Nature, W.H. Freeman and Company, San Francisco, 1982.
- Hutchinson JE. Fractals and self-similarity, Indiana Univ Math J 1981; 30: 713–747.
- Falconer KJ. Fractal Geometry, Mathematical Foundations and Application, John Wiley, 2003.
- Barnsley MF. Fractals Everywhere, Academic Press, Boston, 1988.
- Sidki SN. Regular trees and their automorphisms, Monografias de Matematica 1998; 56.
- Bartholdi L., Grigorchuk R., Nekrashevych V. From Fractal Groups to Fractal Sets. Fractals in Graz, (Peter Grabner and Wolfgang Woess, eds.), Birkhauser Verlag, Basel, 25-118, 2003.
- Nekrashevych V. Self-similar Groups, Mathematical Surveys and Monographs, Amer Math Soc Providence, RI, 117, 2005.
- Demir B., Saltan M. A self-similar group in the sense of iterated function system, Far East J Math Sci 2012; 60(1): 83–99.
- Saltan M, Demir B. Self-similar groups in the sense of an IFS and their properties, Journal of Mathematical Analysis and Applications 2013; 408: 694–704.
- Saltan M., Demir B. An iterated function system for the closure of the adding machine group, Fractals 2015, 23: 1550033.
- Koçak Ş. Kişisel görüşme, 2010.
- Saltan M. The relation between adding machine and p-adic integers, Konuralp Journal of Mathematics 2013; 1 (2): 41-49.
- Robert AM. A Course in p −adic Analysis, Springer, 2000.
Year 2016,
Volume: 4 Issue: 2, 113 - 120, 03.10.2016
Abstract
References
- Mandelbrot BB. The Fractal Geometry of Nature, W.H. Freeman and Company, San Francisco, 1982.
- Hutchinson JE. Fractals and self-similarity, Indiana Univ Math J 1981; 30: 713–747.
- Falconer KJ. Fractal Geometry, Mathematical Foundations and Application, John Wiley, 2003.
- Barnsley MF. Fractals Everywhere, Academic Press, Boston, 1988.
- Sidki SN. Regular trees and their automorphisms, Monografias de Matematica 1998; 56.
- Bartholdi L., Grigorchuk R., Nekrashevych V. From Fractal Groups to Fractal Sets. Fractals in Graz, (Peter Grabner and Wolfgang Woess, eds.), Birkhauser Verlag, Basel, 25-118, 2003.
- Nekrashevych V. Self-similar Groups, Mathematical Surveys and Monographs, Amer Math Soc Providence, RI, 117, 2005.
- Demir B., Saltan M. A self-similar group in the sense of iterated function system, Far East J Math Sci 2012; 60(1): 83–99.
- Saltan M, Demir B. Self-similar groups in the sense of an IFS and their properties, Journal of Mathematical Analysis and Applications 2013; 408: 694–704.
- Saltan M., Demir B. An iterated function system for the closure of the adding machine group, Fractals 2015, 23: 1550033.
- Koçak Ş. Kişisel görüşme, 2010.
- Saltan M. The relation between adding machine and p-adic integers, Konuralp Journal of Mathematics 2013; 1 (2): 41-49.
- Robert AM. A Course in p −adic Analysis, Springer, 2000.
There are 13 citations in total.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | October 3, 2016 |
| Published in Issue | Year 2016 Volume: 4 Issue: 2 |
