On Structurally Stable Diffeomorphisms with Codimension One Expanding Attractors
نویسنده
چکیده
We show that if a closed n-manifold Mn (n ≥ 3) admits a structurally stable diffeomorphism f with an orientable expanding attractor Ω of codimension one, then Mn is homotopy equivalent to the n-torus Tn and is homeomorphic to Tn for n 6= 4. Moreover, there are no nontrivial basic sets of f different from Ω. This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having codimension one orientable expanding attractors and contracting repellers on Tn, n ≥ 3.
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