Rigidity of joinings for some measure preserving systems

Changguang Dong; Adam Kanigowski; Daren Wei

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arXiv · 1812.05483

Rigidity of joinings for some measure preserving systems

Changguang Dong·Adam Kanigowski·Daren Wei

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Abstract

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.

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Changguang Dong, Adam Kanigowski, Daren Wei. 2018-12-13. Rigidity of joinings for some measure preserving systems. https://arxiv.org/abs/1812.05483

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