论文标题
具有等距系数且不弱的Ergodic的非牙本质转换
Nonsingular transformations that are ergodic with isometric coefficients and not weakly doubly ergodic
论文作者
论文摘要
我们研究了无限制和无限措施保护的Ergodic系统的两种特性：具有等距系数的弱双牙型性和牙型性。我们表明，存在具有等距系数的千古化的无限措施转换，但并非弱呈偶性。我们还提供了类型$ \ text {iii}_λ$示例此类系统的示例，$ 0<λ\ leq 1 $。我们证明，在某些假设下，弱混合的系统具有等距系数的厄尔及性，并且在此过程中，我们给出了一个沿序列$（n_i）$的均匀刚性拓扑的动力学系统的示例，该系统无法沿$（N_I）$（N_I）$（N_I）$固定的任何非语言磨性磨性的限制。
We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are ergodic with isometric coefficients but are not weakly doubly ergodic. We also give type $\text{III}_λ$ examples of such systems, $0<λ\leq 1$. We prove that under certain hypotheses, systems that are weakly mixing are ergodic with isometric coefficients and along the way we give an example of a uniformly rigid topological dynamical system along the sequence $(n_i)$ that is not measure theoretically rigid along $(n_i)$ for any nonsingular ergodic finite measure.
