从马尔可夫作用到阿诺索夫流
From Markovian actions to Anosov flows
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中文总结 AI 辅助
研究双叶平面上群作用与拓扑阿诺索夫流的关系，核心方法是证明群作用源于流的充要条件为保定向强马尔可夫作用，主要贡献是建立条件及证明矩形可提升为流的马尔可夫分割。
中文摘要 AI 辅助
在本文中，我们建立了一个关于双叶平面上群作用源于由可定向三维流形支撑的拓扑阿诺索夫流的充要条件。具体而言，我们证明非奇异双叶平面上的群作用源于这样的流，当且仅当它是保定向的强马尔可夫作用，即平面的保定向作用且保持一族满足适当马尔可夫型性质的矩形。此外，我们证明这族矩形可提升为相关流的马尔可夫分割。
英文摘要
In this paper, we establish a necessary and sufficient condition for a group action on a bifoliated plane to arise from a topological Anosov flow supported by an orientable $3$-manifold. More precisely, we show that a group action on a non-singular bifoliated plane arises from such a flow if and only if it is an orientation preserving strong Markovian action, that is, an orientation preserving action of the plane preserving a family of rectangles satisfying suitable Markov-type properties. Furthermore, we prove that this family of rectangles can be lifted to a Markov partition of the associated flow.
