On the Entropy of a Two Step Random Fibonacci Substitution

Abstract

We consider a random generalisation of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping a baa and b ab with probability p and b ba with probability 1-p for 0<p<1 and where the random rule is applied each time it acts on a b. 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.

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