TY - JOUR
T1 - Topological mixing for substitutions on two letters
AU - Kenyon, Richard
AU - Sadun, Lorenzo
AU - Solomyak, Boris
PY - 2005/12
Y1 - 2005/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=27844565864&partnerID=8YFLogxK
U2 - 10.1017/S0143385705000349
DO - 10.1017/S0143385705000349
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AN - SCOPUS:27844565864
SN - 0143-3857
VL - 25
SP - 1919
EP - 1934
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 6
ER -