Spectra and joint dynamics of Poisson suspensions for rank-one automorphisms
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866912106775838720 |
|---|---|
| author | Ryzhikov, Valery V. |
| author_facet | Ryzhikov, Valery V. |
| contents | For every natural $n>1$, there is an operator $T$ of dynamical origin such that its tensor power $T^{\otimes n}$ has singular spectrum, and $T^{\otimes (n+1)}$ has absolutely continuous one. For a set $D$ of positive measure there are mixing zero entropy automorphisms $S,T$ such that $S^nD\cap T^nD=\varnothing$ for all $n>0$. The following answers, in particular, Frantzikinakis-Host's question. If $ p(n+1)- p(n), \ \ q(n+1)- q(n)\ \to\ +\infty$, then there is a divergent sequence $ \sum_{n=1}^{N} μ(S^{ p(n)}C\cap T^{ q(n)}C)/N$ for some set $C$ and automorphisms $S,T$ of simple singular spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02024 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectra and joint dynamics of Poisson suspensions for rank-one automorphisms Ryzhikov, Valery V. Dynamical Systems For every natural $n>1$, there is an operator $T$ of dynamical origin such that its tensor power $T^{\otimes n}$ has singular spectrum, and $T^{\otimes (n+1)}$ has absolutely continuous one. For a set $D$ of positive measure there are mixing zero entropy automorphisms $S,T$ such that $S^nD\cap T^nD=\varnothing$ for all $n>0$. The following answers, in particular, Frantzikinakis-Host's question. If $ p(n+1)- p(n), \ \ q(n+1)- q(n)\ \to\ +\infty$, then there is a divergent sequence $ \sum_{n=1}^{N} μ(S^{ p(n)}C\cap T^{ q(n)}C)/N$ for some set $C$ and automorphisms $S,T$ of simple singular spectrum. |
| title | Spectra and joint dynamics of Poisson suspensions for rank-one automorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2411.02024 |