On structurally stable diffeomorphisms with codimension one expanding attractors

Grines, V.; Zhuzhoma, E.

doi:10.1090/S0002-9947-04-03460-9

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On structurally stable diffeomorphisms with codimension one expanding attractors

Authors: V. Grines and E. Zhuzhoma
Journal: Trans. Amer. Math. Soc. 357 (2005), 617-667
MSC (2000): Primary 37D20; Secondary 37C70, 37C15
Posted: April 16, 2004
MathSciNet review: 2095625
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Abstract: We show that if a closed -manifold $(n\ge 3)$ admits a structurally stable diffeomorphism with an orientable expanding attractor $\Omega$ of codimension one, then is homotopy equivalent to the -torus and is homeomorphic to for $n\ne 4$ . Moreover, there are no nontrivial basic sets of different from $\Omega$ . This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having codimension one orientable expanding attractors and contracting repellers on , $n\ge 3$ .

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