Classifying the expanding attractors on the figure-eight knot exterior and the non-transitive Anosov flows on the Franks-Williams manifold
Classifying the expanding attractors on the figure-eight knot exterior and the non-transitive Anosov flows on the Franks-Williams manifold
复制标题
对 8 字结外部的扩展吸引子和 Franks-Williams 流形上的非传递阿诺索夫流进行分类
DOI：
10.1112/plms.12444
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发表时间：
2022
影响因子：
1.8
通讯作者：
Yu Bin
中科院分区：
文献类型：
--
作者：
Yang Jiagang;Yu Bin
8字形纽结外部N0$N_0$支持一个自然的DA（源自Anosov）扩展吸引子，Franks-Williams利用该吸引子构造了非传递Anosov流的第一个例子。这个流位于一个3流形M0$M_0$中，它是N0$N_0$的二重流形。我们称M0$M_0$为Franks-Williams流形。在本文中，我们证明了，直到轨道等价，这个DA扩展吸引子是唯一的扩展吸引子支持N 0 $N_0 $。证明了在轨道等价条件下，Franks和威廉姆斯构造的非传递Anosov流是唯一的由M0 $M_0 $支持的非传递Anosov流.我们还将这些结果扩展到更一般的背景下。
The figure‐eight knot exterior N0$N_0$ supports a natural DA (derived from Anosov) expanding attractor, with which Franks–Williams constructed the first example of non‐transitive Anosov flow. This flow lies in a 3‐manifold M0$M_0$ which is the double of N0$N_0$. We call M0$M_0$ by the Franks–Williams manifold. In this paper, we prove that, up to orbit‐equivalence, this DA expanding attractor is the unique expanding attractor supported by N0$N_0$. We also show that, up to orbit‐equivalence, the non‐transitive Anosov flow constructed by Franks and Williams is the unique non‐transitive Anosov flow supported by M0$M_0$. We also extend these results to a more general context.