- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 2 Issue: 2
- A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set
A Self-Similar Dendrite with One-Point Intersection and Infinite Post-Critical Set
Authors : Andrei TETENOV, Prabhjot SİNGH
Pages : 70-73
Doi:10.31197/atnaa.417783
View : 4 | Download : 3
Publication Date : 2018-06-30
Article Type : Research
Abstract :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.Keywords : self-similar set, attractor, post-critically finite, open set condition, dendrite