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Rigidity of joinings for some measure-preserving systems
Ergodic Theory and Dynamical Systems ( IF 0.8 ) Pub Date : 2021-04-30 , DOI: 10.1017/etds.2021.34 CHANGGUANG DONG , ADAM KANIGOWSKI , DAREN WEI
Ergodic Theory and Dynamical Systems ( IF 0.8 ) Pub Date : 2021-04-30 , DOI: 10.1017/etds.2021.34 CHANGGUANG DONG , ADAM KANIGOWSKI , DAREN WEI
We introduce two properties: strong R-property and $C(q)$ -property, describing a special way of divergence of nearby trajectories for an abstract measure-preserving system. We show that systems satisfying the strong R-property are disjoint (in the sense of Furstenberg) with systems satisfying the $C(q)$ -property. Moreover, we show that if $u_t$ is a unipotent flow on $G/\Gamma $ with $\Gamma $ irreducible, then $u_t$ satisfies the $C(q)$ -property provided that $u_t$ is not of the form $h_t\times \operatorname {id}$ , where $h_t$ is the classical horocycle flow. Finally, we show that the strong R-property holds for all (smooth) time changes of horocycle flows and non-trivial time changes of bounded-type Heisenberg nilflows.
中文翻译:
一些保量系统的连接刚度
我们引入两个属性:强 R 属性和$C(q)$ -property,描述了抽象度量保持系统附近轨迹的一种特殊发散方式。我们证明满足强 R 属性的系统与满足强 R 属性的系统是不相交的(在 Furstenberg 的意义上)$C(q)$ -财产。此外,我们证明如果$u_t$ 是单能流$G/\伽玛 $ 和$\伽马$ 不可约,则$u_t$ 满足$C(q)$ - 财产前提是$u_t$ 不是形式$h_t\times \operatorname {id}$ , 在哪里$h_t$ 是经典的星环流。最后,我们表明强 R 属性适用于 horocycle 流的所有(平滑)时间变化和有界型 Heisenberg nilflow 的非平凡时间变化。
更新日期:2021-04-30
中文翻译:
一些保量系统的连接刚度
我们引入两个属性:强 R 属性和