Shifts of finite type and random substitutions
Copyright policy )Shifts of finite type and random substitutions
We prove that every topologically transitive shift of finite type in one dimension is topologically conjugate to a subshift arising from a primitive random substitution on a finite alphabet. As a result, we show that the set of values of topological entropy which can be attained by random substitution subshifts contains all Perron numbers and so is dense in the positive real numbers. We also provide an independent proof of this density statement using elementary methods.
- University of Alberta Canada
- Bielefeld University Germany
Random substitutions, topological entropy, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 37B10, 37A50, 37B40, 52C23, shifts of finite type
Random substitutions, topological entropy, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, 37B10, 37A50, 37B40, 52C23, shifts of finite type
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