On the Entropy of a Family of Random Substitutions

Abstract

The generalised random Fibonacci chain is a stochastic extension of the classical Fibonacci substitution and is defined as the rule mapping $0\mapsto 1$ and $1\mapsto 1^{i}01^{m-i}$ with probability $p_i$, where $p_i\ge 0$ with ${\sum }_{i=0}^m{p}_i=1$, and where the random rule is applied each time it acts on a 1. We show that the topological entropy of this object is given by the growth rate of the set of inflated generalised random Fibonacci words.

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References in corpus (2)

• Kinematic Diffraction from a Mathematical Viewpoint
• On the Entropy of Random Fibonacci Words

Cited by in corpus (6)

• Dynamical systems arising from random substitutions
• Inflation word entropy for semi-compatible random substitutions
• On a Family of Random Noble Means Substitutions
• On the Entropy of a Two Step Random Fibonacci Substitution
• Periodic points in random substitution subshifts
• Topology of the Random Fibonacci Tiling Space