论文标题
部分可观测时空混沌系统的无模型预测
Anosov flows and Liouville pairs in dimension three
论文作者
论文摘要
在Mitsumatsu和Hozoori的工作的基础上，我们建立了三维Anosov流与某些我们称为Anosov Liouville Pairs的一对触点形式之间的完整同型对应关系。我们展示了Anosov流和双接触结构之间的相似对应关系，从而扩展了Mitsumatsu和Eliashberg-Thurston的工作。结果，每个Anosov在封闭式的三个manifold $ m $上的流动都会引起$ \ mathbb {r} \ times m $上的liouville结构，该结构已定义为同型，这仅取决于Anosov Flow的同型类别。我们的结果还为Anosov流动在维度第三的分类问题提供了新的观点。
Building upon the work of Mitsumatsu and Hozoori, we establish a complete homotopy correspondence between three-dimensional Anosov flows and certain pairs of contact forms that we call Anosov Liouville pairs. We show a similar correspondence between projectively Anosov flows and bi-contact structures, extending the work of Mitsumatsu and Eliashberg-Thurston. As a consequence, every Anosov flow on a closed oriented three-manifold $M$ gives rise to a Liouville structure on $\mathbb{R} \times M$ which is well-defined up to homotopy, and which only depends on the homotopy class of the Anosov flow. Our results also provide a new perspective on the classification problem of Anosov flows in dimension three.
