TY - JOUR
T1 - Tori with hyperbolic dynamics in 3-manifolds
AU - Hertz, Federico Rodriguez
AU - Hertz, Maria Alejandra Rodriguez
AU - Ures, RaúL
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2011/1
Y1 - 2011/1
N2 - 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: π1 (T) → π1 (T) is hyperbolic. We prove that only few irreducible 3-manifolds admit Anosov tori: (1) the 3-torus T3; (2) the mapping torus of-Id; and (3) the mapping tori of hyperbolic automorphisms of T2. This has consequences for instance in the context of partially hyperbolic dynamics of 3-manifolds: if there is an invariant foliation. Tcu tangent to the center-unstable bundle Ec⊕Eu, then Tcu 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].
AB - 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: π1 (T) → π1 (T) is hyperbolic. We prove that only few irreducible 3-manifolds admit Anosov tori: (1) the 3-torus T3; (2) the mapping torus of-Id; and (3) the mapping tori of hyperbolic automorphisms of T2. This has consequences for instance in the context of partially hyperbolic dynamics of 3-manifolds: if there is an invariant foliation. Tcu tangent to the center-unstable bundle Ec⊕Eu, then Tcu 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].
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U2 - 10.3934/jmd.2011.5.185
DO - 10.3934/jmd.2011.5.185
M3 - Article
AN - SCOPUS:79955439398
SN - 1930-5311
VL - 5
SP - 185
EP - 202
JO - Journal of Modern Dynamics
JF - Journal of Modern Dynamics
IS - 1
ER -