Confined Poisson extensions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918063300935680 |
|---|---|
| author | Benzoni, Séverin Roy, Emmanuel de la Rue, Thierry |
| author_facet | Benzoni, Séverin Roy, Emmanuel de la Rue, Thierry |
| contents | This paper follows on from our previous work, where we introduced the notion of \emph{confined extensions}, and our purpose is to widen the context in which such extensions appear. We do so in the setup of Poisson suspensions: we take a $σ$-finite measure-preserving dynamical system $(X, μ, T)$ and a compact extension $(X \times G, μ\otimes m_G, T_ϕ)$, then we consider the corresponding Poisson extension $((X \times G)^*, (μ\otimes m_G)^*, (T_ϕ)_*) \overset{}{\to} (X^*, μ^*, T_*)$. Our results give two different conditions under which that extension is confined. Finally, to show that those conditions are not void, we give an example of a system $(X, μ, T)$ and a cocycle $ϕ$ so that the compact extension $(X \times G, μ\otimes m_G, T_ϕ)$ has an infinite ergodic index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Confined Poisson extensions Benzoni, Séverin Roy, Emmanuel de la Rue, Thierry Dynamical Systems Probability This paper follows on from our previous work, where we introduced the notion of \emph{confined extensions}, and our purpose is to widen the context in which such extensions appear. We do so in the setup of Poisson suspensions: we take a $σ$-finite measure-preserving dynamical system $(X, μ, T)$ and a compact extension $(X \times G, μ\otimes m_G, T_ϕ)$, then we consider the corresponding Poisson extension $((X \times G)^*, (μ\otimes m_G)^*, (T_ϕ)_*) \overset{}{\to} (X^*, μ^*, T_*)$. Our results give two different conditions under which that extension is confined. Finally, to show that those conditions are not void, we give an example of a system $(X, μ, T)$ and a cocycle $ϕ$ so that the compact extension $(X \times G, μ\otimes m_G, T_ϕ)$ has an infinite ergodic index. |
| title | Confined Poisson extensions |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2403.13416 |