Topological mixing for substitutions on two letters
Richard Wallace Kenyon, Lorenzo Sadun, Boris Solomyak · Ergodic Theory and Dynamical Systems · 2005
We investigate topological mixing for $\mathbb Z$ and $\mathbb R$ actions associated with primitive substitutions on two letters. The characterization is complete if the second eigenvalue $\theta_2$ of the substitution matrix satisfies $|\theta_2| e 1$ . If $|\theta_2| 1$ , then topological mixing is equivalent to topological weak mixing, which has an explicit arithmetic characterization. The case $|\theta_2|=1$ is more delicate, and we only obtain some partial results.