On structurally stable diffeomorphisms with codimension one expanding attractors

Grines, V.; Zhuzhoma, E.

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

On structurally stable diffeomorphisms with codimension one expanding attractors
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by V. Grines and E. Zhuzhoma

Trans. Amer. Math. Soc. 357 (2005), 617-667

DOI: https://doi.org/10.1090/S0002-9947-04-03460-9

Published electronically: April 16, 2004

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Abstract:

We show that if a closed $n$-manifold $M^n$ $(n\ge 3)$ admits a structurally stable diffeomorphism $f$ with an orientable expanding attractor $\Omega$ of codimension one, then $M^n$ is homotopy equivalent to the $n$-torus $T^n$ and is homeomorphic to $T^n$ for $n\ne 4$. Moreover, there are no nontrivial basic sets of $f$ different from $\Omega$. This allows us to classify, up to conjugacy, structurally stable diffeomorphisms having codimension one orientable expanding attractors and contracting repellers on $T^n$, $n\ge 3$.

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