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On the Entropy of a Two Step Random Fibonacci Substitution
Department of Mathematics, Universität Bielefeld, Postfach 100131, D–33501 Bielefeld, Germany
Received: 8 July 2013; in revised form: 30 July 2013 / Accepted: 19 August 2013 / Published: 23 August 2013
Abstract: We consider a random generalization of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping, a → baa and b → ab, with probability , and → ba, with probability 1 – p for 0 < p < 1, and where the random rule is applied each time it acts on a . We show that the topological entropy of this object is given by the growth rate of the set of inflated random Fibonacci words, and we exactly calculate its value.
Keywords: combinatorics on words; asymptotic enumeration; symbolic dynamics
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MDPI and ACS Style
Nilsson, J. On the Entropy of a Two Step Random Fibonacci Substitution. Entropy 2013, 15, 3312-3324.
Nilsson J. On the Entropy of a Two Step Random Fibonacci Substitution. Entropy. 2013; 15(9):3312-3324.
Nilsson, Johan. 2013. "On the Entropy of a Two Step Random Fibonacci Substitution." Entropy 15, no. 9: 3312-3324.