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- Title
On Surface Attractors and Repellers in 3-Manifolds.
- Authors
Grines, V. Z.; Medvedev, V. S.; Zhuzhoma, E. V.
- Abstract
We show that if f: M 3 → M 3 is an A diffeomorphism with a surface two-dimensional attractor or repeller $$\mathcal{B}$$ with support $$M_\mathcal{B}^2$$ , then $$\mathcal{B} = M_\mathcal{B}^2$$ and there exists a k ≥ 1 such that (1) $$M_\mathcal{B}^2$$ is the disjoint union M ⋃ ⋯ ⋃ M of tame surfaces such that each surface M is homeomorphic to the 2-torus T 2; (2) the restriction of f k to M , i ∈ {1,..., k}, is conjugate to an Anosov diffeomorphism of the torus T 2.
- Subjects
MANIFOLDS (Mathematics); DIFFERENTIAL geometry; TOPOLOGY; DIFFEOMORPHISMS; ANOSOV flows
- Publication
Mathematical Notes, 2005, Vol 78, Issue 5/6, p757
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1007/s11006-005-0181-1