2 4 Ju n 20 04 TOPOLOGICAL MIXING FOR SUBSTITUTIONS ON TWO LETTERS
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چکیده
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| 6= 1. If |θ2| < 1, 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.
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2 2 Ju l 2 00 5 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| 6= 1. If |θ2| < 1, 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 mixi...
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تاریخ انتشار 2004