A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set
Keywords:
self-similar set, attractor, post-critically finite, open set condition, dendriteAbstract
We build an example of a system S of similarities in R^2 whose attractor is a plane dendrite K⊃[0,1]�⊃[0,1] which satisfies one point intersection property, while the post-critical set of the system S is a countable set whose natural projection to K is dense in the middle-third Cantor set.
References
C. Bandt, N.V. Hung and H. Rao, On the open set condition for self-similar fractals, Proc. Amer. Math. Soc. 134 (2005), 1369-1374
Charatonik J., Charatonik W., Dendrites, Aportaciones Mat. Comun. 22 (1998), 227-253.
Hutchinson, J.E. Fractals and self-similarity. Indiana Univ. Math. J 30, 1981, 713-747
Kigami, J. Analysis on Fractals. Cambridge University Press, 2001
P.A.P. Moran, Additive functions of intervals and Hausdor measure Proc. Cambridge Philos. Soc. 42 (1946), 15-23
