Abstract
We show that if Λ is a codimension-one hyperbolic attractor for a Cr diffeomorphism f, where 2 ⩽ r ⩽ ∞, and f is not Anosov, then there is a neighborhood 𝒰 of f in Diffr(M) and an open and dense set 𝒱 of 𝒰 such that any g ∈ 𝒱 has a trivial centralizer on the basin of attraction for Λ.
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