Topological mixing for substitutions on two letters

We investigate topological mixing for ℤ and ℝ actions associated with primitive substitutions on two letters. The characterization is complete if the second eigenvalue θ₂ of the substitution matrix satisfies |θ₂| ≠ 1. If |θ₂|, then (as is well known) the substitution system is not topologically weak mixing, so it is not topologically mixing. We prove that if |θ₂| > 1, then topological mixing is equivalent to topological weak mixing, which has an explicit arithmetic characterization. The case |θ₂| = 1 is more delicate, and we only obtain some partial results.