Denker-Sato type Markov chains on self-similar sets (Q2349901)

The authors consider a Denker-Sato type Markov chains associated with self-similar sets. These chains are defined on the augmented tree of the symbolic space. The main result is the theorem: Let \(\{S_j\}^{N}_{j=1}\) be an iterated function system satisfying the open set condition, and \(K\) be the associated self-similar set. Assume that the system is equipped with a Denker-Sato type Markov chain on the augmented tree of the symbolic space. Then the Martin boundary, the hyperbolic boundary, and the set \(K\) are homeomorphic.