On the Topological Entropy of the Discretized Markov β-Transformations

Hiroshi FUJISAKI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.12   pp.2238-2247
Publication Date: 2016/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.2238
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Fundamentals of Information Theory
Keyword: 
topological entropy,  discretized Markov transformation,  β-transformation,  full length sequence,  

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Summary: 
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≤ck-1) of (k-c) forbidden blocks, whose underlying transformations exhibit a wide class of greedy β-expansions of real numbers.