A class of continua that are not attractors of any IFS

• Autorzy: Marcin Kulczycki , Magdalena Nowak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Fractal; Continuum; Iterated function system; Attractor

Kategorie tematyczne

• 54H20: Topological dynamics
• 54F15: Continua and generalizations
• 37B25: Lyapunov functions and stability; attractors, repellers
• 28A80: Fractals

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 2073-2076

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Marcin Kulczycki

• Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348, Kraków, Poland

autor

Magdalena Nowak

Bibliografia

• [1] Barnsley M., Fractals Everywhere, Academic Press, Boston, 1988
• [2] Edelstein M., On fixed and periodic points under contractive mappings, J. Lond. Math. Soc., 1962, 37, 74–79 http://dx.doi.org/10.1112/jlms/s1-37.1.74[Crossref]
• [3] Hata M., On the structure of self-similar sets, Japan J. Appl. Math., 1985, 2(2), 381–414 http://dx.doi.org/10.1007/BF03167083[Crossref]
• [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
• [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

Identyfikatory

DOI

10.2478/s11533-012-0108-5