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 -