Rigidity of joinings for some measure-preserving systems
| Autor: | Daren Wei, Changguang Dong, Adam Kanigowski |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics 010102 general mathematics Rigidity (psychology) Disjoint sets Unipotent 01 natural sciences Measure (mathematics) Bounded type Horocycle Flow (mathematics) 0103 physical sciences 010307 mathematical physics 0101 mathematics Divergence (statistics) Mathematics |
| Zdroj: | Ergodic Theory and Dynamical Systems. 42:665-690 |
| ISSN: | 1469-4417 0143-3857 |
| DOI: | 10.1017/etds.2021.34 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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