论文标题
关于零熵的拓扑模型，松散的伯努利系统
On topological models of zero entropy loosely Bernoulli systems
论文作者
论文摘要
我们提供了独特的千古拓扑动力学系统（TDSS）的纯粹拓扑表征，其独特的不变度量是零熵宽松的bernoulli（随后，我们称之为宽松的kronecker）。我们的证明的核心是Feldman-Katok的连续性（简称FK-CONTINUSINE），也就是说，对于Feldman-Katok伪计的变化，连续性。 Feldman-Katok伪计是符号系统F型杆（编辑）度量的拓扑类似物。我们还研究了FK-continition，fk敏感性的相反。我们获得了Auslander-Yorke二分法的版本：最小的TDS是FK连续的或对FK敏感的，并且透射式TDS几乎是FK-collinubule的或FK敏感的。
We provide a purely topological characterisation of uniquely ergodic topological dynamical systems (TDSs) whose unique invariant measure is zero entropy loosely Bernoulli (following Ratner, we call such measures loosely Kronecker). At the heart of our proofs lies Feldman-Katok continuity (FK-continuity for short), that is, continuity with respect to the change of metric to the Feldman-Katok pseudometric. Feldman-Katok pseudometric is a topological analog of f-bar (edit) metric for symbolic systems. We also study an opposite of FK-continuity, coined FK-sensitivity. We obtain a version of Auslander-Yorke dichotomies: minimal TDSs are either FK-continuous or FK-sensitive, and transitive TDSs are either almost FK-continuous or FK-sensitive.
