In this note we prove that Moebius orthogonality does not hold for subshifts of finite type with positive topological entropy. This, in particular, shows that all C 1+α surface diffeomorphisms with positive entropy correlate with the Moebius function.
In [5] Bourgain proves that Sarnak's disjointness conjecture holds for a certain class of Three-interval exchange maps. In the present paper we slightly improve the Diophantine condition of Bourgain and estimate the constants in the proof. We further show, that the new parameter set has positive, but not full Hausdorff dimension. This, in particular, implies that the Lebesgue measure of this set is zero. n k=1 µ(k)f (k) = o(1),as According to [10], if (α, β) ∈ D 0 is not in D and is not on any of the rational lines pα + qβ = p − q, pα + qβ = p − q + 1, pα + qβ = p − q − 1, then there exists a unique finite sequence of integers l 0 , l 1 , ..., l k such that (α, β) is in H −
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