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。