### Abstract

Let M be a closed orientable irreducible 3-dimensional manifold. An embedded 2-torus T is an Anosov torus if there exists a diffeomorphism f over M for which T is f-invariant and f#T: π_{1} (T) → π_{1} (T) is hyperbolic. We prove that only few irreducible 3-manifolds admit Anosov tori: (1) the 3-torus T^{3}; (2) the mapping torus of-Id; and (3) the mapping tori of hyperbolic automorphisms of T^{2}. This has consequences for instance in the context of partially hyperbolic dynamics of 3-manifolds: if there is an invariant foliation. T^{cu} tangent to the center-unstable bundle E^{c}⊕E^{u}, then T^{cu} has no compact leaves [21]. This has led to the first example of a non-dynamically coherent partially hyperbolic diffeomorphism with one-dimensional center bundle [21].

Original language | English (US) |
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Pages (from-to) | 185-202 |

Number of pages | 18 |

Journal | Journal of Modern Dynamics |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2011 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Algebra and Number Theory
- Applied Mathematics

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## Cite this

*Journal of Modern Dynamics*,

*5*(1), 185-202. https://doi.org/10.3934/jmd.2011.5.185