Discretized Markov Transformations--An Example of Ultradiscrete Dynamical Systems--

Hiroshi FUJISAKI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.10   pp.2684-2691
Publication Date: 2005/10/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.10.2684
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: 
Keyword: 
discretized Markov transformations,  maximal-period sequences,  

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Summary: 
We define discretized Markov transformations and find an algorithm to give the number of maximal-period sequences based on discretized Markov transformations. In this report, we focus on the discretized dyadic transformations and the discretized golden mean transformations. Then we find an algorithm to give the number of maximal-period sequences based on these discretized transformations. Moreover, we define a number-theoretic function related to the numbers of maximal-period sequences based on these discretized transformations. We also introduce the entropy of the maximal-period sequences based on these discretized transformations.