论文标题
离散化Anosov流动的全球稳定性
Global stability of discretized Anosov flows
论文作者
论文摘要
本文的目的是建立一类称为\ emph {iveptized anosov flow}的一类大量部分双曲线差异的一般属性。提出了这些系统的一般定义，并被证明与[BFFP19]中引入的定义以及流动类型的概念相当于[BFT20]中引入的部分双曲线差异性。 一组离散的Anosov流显示为$ c^1 $打开，并在部分双曲线差异性内封闭。所有离散的Anosov流都被证明是动态连贯和斑块膨胀的。显示中心束的唯一集成性是针对整个连接组件发生的，尤其是包含Anosov流的时间1映射的组件。对于一般连接的组件，获得了不变叶的独特性的结果。 对于统一的紧凑型中心叶叶，延伸[BB16]中的研究的部分双曲线系统也会发现类似的结果。
The goal of this article is to establish several general properties of a somewhat large class of partially hyperbolic diffeomorphisms called \emph{discretized Anosov flows}. A general definition for these systems is presented and is proven to be equivalent with the definition introduced in [BFFP19], as well as with the notion of flow type partially hyperbolic diffeomorphisms introduced in [BFT20]. The set of discretized Anosov flows is shown to be $C^1$ open and closed inside the set of partially hyperbolic diffeomorphisms. Every discretized Anosov flow is proven to be dynamically coherent and plaque expansive. Unique integrability of the center bundle is shown to happen for whole connected components, notably the ones containing the time 1 map of an Anosov flow. For general connected components, a result on uniqueness of invariant foliation is obtained. Similar results are seen to happen for partially hyperbolic systems admitting a uniformly compact center foliation extending the studies initiated in [BB16].
