Dynamical incoherence for a large class of partially hyperbolic diffeomorphisms
Dynamical incoherence for a large class of partially hyperbolic diffeomorphisms
复制标题
一类部分双曲微分同胚的动力学不相干
DOI：
10.1017/etds.2020.113
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发表时间：
2021
影响因子：
0.9
通讯作者：
POTRIE, RAFAEL
中科院分区：
文献类型：
--
作者：
BARTHELMÉ, THOMAS;FENLEY, SERGIO R.;FRANKEL, STEVEN;POTRIE, RAFAEL
我们表明，如果一个部分双曲的Seifert流形的双同态诱导的映射在基地有一个伪Anosov组件，那么它不能是动态相干的。这扩展了[C。Bonatti，A. Gogolev，A. Hammerlindl和R.波特里反常的部分双曲同态III：abstraction和不相干。托波尔，在整个isotopy类中出现。我们将这些技巧应用于双曲三维流形中某些部分双曲同态的研究。Barthelmé，S. Fenley，S. Frankel和R.波特里同伦于三维恒等式的部分双曲双同态，第一部分：动力相干情形。预印本，2019年，arXiv：1908.06227;部分双曲同伦的身份在3维，第二部分：分支叶理。预印本，2020，arXiv：2008.04871]。附录回顾了一些后果的尼尔森-瑟斯顿分类的表面同胚的动力学升降机等地图的普遍覆盖。
We show that if a partially hyperbolic diffeomorphism of a Seifert manifold induces a map in the base which has a pseudo-Anosov component then it cannot be dynamically coherent. This extends [C. Bonatti, A. Gogolev, A. Hammerlindl and R. Potrie. Anomalous partially hyperbolic diffeomorphisms III: Abundance and incoherence. Geom. Topol., to appear] to the whole isotopy class. We relate the techniques to the study of certain partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds performed in [T. Barthelmé, S. Fenley, S. Frankel and R. Potrie. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, part I: The dynamically coherent case. Preprint, 2019, arXiv:1908.06227; Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, part II: Branching foliations. Preprint, 2020, arXiv: 2008.04871]. The appendix reviews some consequences of the Nielsen–Thurston classification of surface homeomorphisms for the dynamics of lifts of such maps to the universal cover.