On the Entropy of a Two Step Random Fibonacci Substitution

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