Minimal subdynamics and minimal flows without characteristic measures
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911876037738496 |
|---|---|
| author | Frisch, Joshua Seward, Brandon Zucker, Andy |
| author_facet | Frisch, Joshua Seward, Brandon Zucker, Andy |
| contents | Given a countable group $G$ and a $G$-flow $X$, a measure $μ\in P(X)$ is called characteristic if it is $\mathrm{Aut}(X, G)$-invariant. Frisch and Tamuz asked about the existence of a minimal $G$-flow, for any group $G$, which does not admit a characteristic measure. We construct for every countable group $G$ such a minimal flow. Along the way, we are motivated to consider a family of questions we refer to as minimal subdynamics: Given a countable group $G$ and a collection of infinite subgroups $\{Δ_i: i\in I\}$, when is there a faithful $G$-flow for which every $Δ_i$ acts minimally? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_04875 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Minimal subdynamics and minimal flows without characteristic measures Frisch, Joshua Seward, Brandon Zucker, Andy Dynamical Systems Given a countable group $G$ and a $G$-flow $X$, a measure $μ\in P(X)$ is called characteristic if it is $\mathrm{Aut}(X, G)$-invariant. Frisch and Tamuz asked about the existence of a minimal $G$-flow, for any group $G$, which does not admit a characteristic measure. We construct for every countable group $G$ such a minimal flow. Along the way, we are motivated to consider a family of questions we refer to as minimal subdynamics: Given a countable group $G$ and a collection of infinite subgroups $\{Δ_i: i\in I\}$, when is there a faithful $G$-flow for which every $Δ_i$ acts minimally? |
| title | Minimal subdynamics and minimal flows without characteristic measures |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2203.04875 |