强秩1变换的近连续偶Kakutani等价
Nearly Continuous Even Kakutani Equivalence of Strongly Rank One Transformations
摘要：
在遍历论中，如果两个系统的诱导变换之间存在共轭，则两个系统是角谷等价的。在《测度拓扑轨道与角谷等价》中，德尔·容克、鲁道夫和韦斯将几乎连续的甚至角谷等价定义为一个轨道等价，它限制于几乎闭集上的诱导映射之间的共轭。本文将两个近似连续动力系统之间的近似连续偶Kakutani等价定义为相同大小的近似闭集上的诱导映射之间的近似连续共轭，并证明了这个定义等价于del Junco，Rudolph和Weiss给出的定义.本文证明了，在一个附加的限制条件下，如果两个系统几乎连续（非偶）Kakutani等价，则其中一个系统同构于另一个系统的诱导变换，并利用这个结果证明了一类包含Chacon映射的强秩1变换与无理旋转属于同一个几乎连续偶Kakutani等价类.
英文摘要：
In ergodic theory, two systems are Kakutani equivalent if there exists a conjugacy between induced transformations. In Measured Topological Orbit and Kakutani Equivalence, del Junco, Rudolph, and Weiss defined nearly continuous even Kakutani equivalence as an orbit equivalence which restricts to a conjugacy between induced maps on nearly clopen sets. This paper defines nearly continuous even Kakutani equivalence between two nearly continuous dynamical systems as a nearly continuous conjugacy between induced maps on nearly clopen sets of the same size and shows that this definition is equivalent to the definition given by del Junco, Rudolph, and Weiss. The paper shows that, with an added restriction, if two systems are nearly continuously (non-even) Kakutani equivalent, then one system is isomorphic to an induced transformation of the other, and uses this result to prove that a class of transformations called strongly rank one and containing Chacon's map belongs to the same nearly continuous even Kakutani equivalence class as irrational rotations.
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