A class of continua that are not attractors of any IFS
Marcin Kulczycki; Magdalena Nowak
Open Mathematics (2012)
- Volume: 10, Issue: 6, page 2073-2076
- ISSN: 2391-5455
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topMarcin Kulczycki, and Magdalena Nowak. "A class of continua that are not attractors of any IFS." Open Mathematics 10.6 (2012): 2073-2076. <http://eudml.org/doc/269096>.
@article{MarcinKulczycki2012,
abstract = {This paper presents a sufficient condition for a continuum in ℝn to be embeddable in ℝn in such a way that its image is not an attractor of any iterated function system. An example of a continuum in ℝ2 that is not an attractor of any weak iterated function system is also given.},
author = {Marcin Kulczycki, Magdalena Nowak},
journal = {Open Mathematics},
keywords = {Fractal; Continuum; Iterated function system; Attractor; fractal; continuum; iterated function system; attractor},
language = {eng},
number = {6},
pages = {2073-2076},
title = {A class of continua that are not attractors of any IFS},
url = {http://eudml.org/doc/269096},
volume = {10},
year = {2012},
}
TY - JOUR
AU - Marcin Kulczycki
AU - Magdalena Nowak
TI - A class of continua that are not attractors of any IFS
JO - Open Mathematics
PY - 2012
VL - 10
IS - 6
SP - 2073
EP - 2076
AB - This paper presents a sufficient condition for a continuum in ℝn to be embeddable in ℝn in such a way that its image is not an attractor of any iterated function system. An example of a continuum in ℝ2 that is not an attractor of any weak iterated function system is also given.
LA - eng
KW - Fractal; Continuum; Iterated function system; Attractor; fractal; continuum; iterated function system; attractor
UR - http://eudml.org/doc/269096
ER -
References
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- [4] Hutchinson J.E., Fractals and self similarity, Indiana Univ. Math. J., 1981, 30(5), 713–747 http://dx.doi.org/10.1512/iumj.1981.30.30055[Crossref]
- [5] Kwiecinski M., A locally connected continuum which is not an IFS attractor, Bull. Pol. Acad. Sci. Math., 1999, 47(2), 127–132 Zbl0931.54028
- [6] Sanders M.J., Non-attractors of iterated fuction systems, Texas Project NexT Journal, 2003, 1, 1–9
- [7] Sanders M.J., An n-cell in ℝn+1 that is not the attractor of any IFS on ℝn+1, Missouri J. Math. Sci., 2009, 21(1), 13–20 Zbl1175.37026
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