A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set

Yıl 2018, , 70 - 73, 30.06.2018

Andrei Tetenov , Prabhjot Singh

https://doi.org/10.31197/atnaa.417783

Öz

We build an example of a system S of similarities in R^2 whose attractor is a plane dendrite $K\supset [0,1]$ 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.

Anahtar Kelimeler

self-similar set, attractor, post-critically finite, open set condition, dendrite

Kaynakça

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• 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