Multipliers and Disjointness from Mixing
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914472453472256 |
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| author | Farhangi, Sohail Moreira, Joel Zelada, Rigoberto |
| author_facet | Farhangi, Sohail Moreira, Joel Zelada, Rigoberto |
| contents | In 2005, Parreau proved that if a measure preserving system is not strongly mixing then it contains a non-trivial factor that is disjoint from every strongly mixing system. Taking this construction as the starting point, we develop the complementary notions of $\mathcal U$-generated and $\mathcal U$-mixing systems, for a set $\mathcal U$ of ultrafilters, and use them to recover several classical results in ergodic theory as special cases of a unified framework. We prove that a system is $\mathcal U$-mixing if and only if it is disjoint from all $\mathcal U$-generated systems. In fact, we show that if $\mathcal Y$ is a $\mathcal U$-generated system and $\mathcal Z$ is disjoint from every $\mathcal U$-mixing system, then any joining of $\mathcal Y$ and $\mathcal Z$ remains disjoint from all $\mathcal U$-mixing systems. We also show that every partially rigid system is a finite extension of some $\mathcal{U}$-generated system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12915 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multipliers and Disjointness from Mixing Farhangi, Sohail Moreira, Joel Zelada, Rigoberto Dynamical Systems Spectral Theory In 2005, Parreau proved that if a measure preserving system is not strongly mixing then it contains a non-trivial factor that is disjoint from every strongly mixing system. Taking this construction as the starting point, we develop the complementary notions of $\mathcal U$-generated and $\mathcal U$-mixing systems, for a set $\mathcal U$ of ultrafilters, and use them to recover several classical results in ergodic theory as special cases of a unified framework. We prove that a system is $\mathcal U$-mixing if and only if it is disjoint from all $\mathcal U$-generated systems. In fact, we show that if $\mathcal Y$ is a $\mathcal U$-generated system and $\mathcal Z$ is disjoint from every $\mathcal U$-mixing system, then any joining of $\mathcal Y$ and $\mathcal Z$ remains disjoint from all $\mathcal U$-mixing systems. We also show that every partially rigid system is a finite extension of some $\mathcal{U}$-generated system. |
| title | Multipliers and Disjointness from Mixing |
| topic | Dynamical Systems Spectral Theory |
| url | https://arxiv.org/abs/2604.12915 |