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1992 | 141 | 3 | 257-268
Tytuł artykułu

Topological spaces admitting a unique fractal structure

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Each homeomorphism from the n-dimensional Sierpiński gasket into itself is a similarity map with respect to the usual metrization. Moreover, the topology of this space determines a kind of Haar measure and a canonical metric. We study spaces with similar properties. It turns out that in many cases, "fractal structure" is not a metric but a topological phenomenon.
Słowa kluczowe
Rocznik
Tom
141
Numer
3
Strony
257-268
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-11-11
poprawiono
1992-03-17
Twórcy
  • Mathematics Department, Addis Ababa University D-O-2200 Greifswald, P.O. Box 1176, Addis Ababa, Ethiopia
autor
  • Fachbereich Mathematik, Ernst-Moritz-Arndt-Universität, Germany
Bibliografia
  • [1] C. Bandt and K. Keller, Self-similar sets 2. A simple approach to the topological structure of fractals, Math. Nachr. 154 (1991), 27-39.
  • [2] C. Bandt and K. Keller, Symbolic dynamics for angle-doubling on the circle I. The topology of locally connected Julia sets, in: U. Krengel, K. Richter and V. Warstat (eds.), Ergodic Theory and Related Topics III, Lecture Notes in Math. 1514, Springer, 1992, 1-23.
  • [3] C. Bandt and T. Kuschel, Self-similar sets 8. Average interior distance in some fractals, Proc. Measure Theory Conference, Oberwolfach 1990, Rend. Circ. Mat. Palermo (2) Suppl. 28 (1992), 307-317.
  • [4] C. Bandt and T. Retta, Self-similar sets as inverse limits of finite topological spaces, in: C. Bandt, J. Flachsmeyer and H. Haase (eds.), Topology, Measures and Fractals, Akademie-Verlag, Berlin 1992, 41-46.
  • [5] C. Bandt and J. Stahnke, Self-similar sets. 6. Interior distance on deterministic fractals, preprint, Greifswald 1990.
  • [6] M. T. Barlow and E. A. Perkins, Brownian motion on the Sierpiński gasket, Probab. Theory Related Fields 79 (1988), 543-623.
  • [7] P. F. Duvall, J. W. Emert and L. S. Husch, Iterated function systems, compact semigroups and topological contractions, preprint, University of North Carolina, 1990.
  • [8] K. J. Falconer, Fractal Geometry, Wiley, 1990.
  • [9] J. de Groot, Groups represented as homeomorphism groups I, Math. Ann. 138 (1959), 80-102.
  • [10] M. Hata, On the structure of self-similar sets, Japan J. Appl. Math. 2 (2) (1985), 381-414.
  • [11] A. Hinz and A. Schief, The average distance on the Sierpiński gasket, Probab. Theory Related Fields 87 (1990), 129-138.
  • [12] V. Kannan and M. Rajagopalan, Constructions and applications of rigid spaces, I, Adv. in Math. 29 (1978), 89-130; II, Amer. J. Math. 100 (1978), 1139-1172.
  • [13] J. Kigami, A harmonic calculus on the Sierpiński spaces, Japan J. Appl. Math. 6 (2) (1989), 259-290.
  • [14] J. Kigami, Harmonic calculus on p.c.f. self-similar sets, Trans. Amer. Math. Soc., to appear.
  • [15] K. Kuratowski, Topology, Vol. 2, Polish Scientific Publishers and Academic Press, 1968.
  • [16] T. Lindstrøm, Brownian motion on nested fractals, Mem. Amer. Math. Soc. 83 (1990).
  • [17] C. Penrose, On quotients of the shift associate with dendritic Julia sets of quadratic polynomials, Ph.D. thesis, University of Warwick, 1990.
  • [18] W. Rinow, Die innere Geometrie der metrischen Räume, Grundlehren Math. Wiss. 105, Springer, 1961.
  • [19] W. P. Thurston, On the combinatorics and dynamics of iterated rational maps, preprint, Princeton 1985.
  • [20] W. Dębski and J. Mioduszewski, simple plane images of the Sierpiński triangular curve are nowhere dense}, Colloq. Math. 59 (1990), 125-140.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv141i3p257bwm
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