On non-orientable two-dimensional basic sets on~3-manifolds
Sbornik. Mathematics, Tome 193 (2002) no. 6, pp. 869-888

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It is proved that a structurally stable diffeomorphism $f\colon M^3\to M^3$ of a closed three-dimensional manifold $M^3$ does not contain in the spectral decomposition non-orientable expanding attractors or contracting repellers of codimension one.
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     author = {E. V. Zhuzhoma and V. S. Medvedev},
     title = {On non-orientable two-dimensional basic sets on~3-manifolds},
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E. V. Zhuzhoma; V. S. Medvedev. On non-orientable two-dimensional basic sets on~3-manifolds. Sbornik. Mathematics, Tome 193 (2002) no. 6, pp. 869-888. http://geodesic.mathdoc.fr/item/SM_2002_193_6_a4/