Topological mixing for substitutions on two letters

Richard Kenyon, Lorenzo Sadun, Boris Solomyak

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish
Pages (from-to)1919-1934
Number of pages16
JournalErgodic Theory and Dynamical Systems
Issue number6
StatePublished - Dec 2005
Externally publishedYes


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