On the Topological Entropy of the Discretized Markov β-Transformations

Abstract

We define the topological entropy of the discretized Markov transformations. Previously, we obtained the topological entropy of the discretized dyadic transformation. In this research, we obtain the topological entropy of the discretized golden mean transformation. We also generalize this result and give the topological entropy of the discretized Markov β-transformations with the alphabet Σ={0,1,…,k-1} and the set F={(k-1)c,…,(k-1)(k-1)}(1≤c≤k-1) of (k-c) forbidden blocks, whose underlying transformations exhibit a wide class of greedy β-expansions of real numbers.