Confined Poisson extensions
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| Název: | Confined Poisson extensions |
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| Autoři: | Benzoni, Séverin, Roy, Emmanuel, de la Rue, Thierry |
| Zdroj: | Discrete and Continuous Dynamical Systems. 46:433-453 |
| Publication Status: | Preprint |
| Informace o vydavateli: | American Institute of Mathematical Sciences (AIMS), 2026. |
| Rok vydání: | 2026 |
| Témata: | Probability (math.PR), FOS: Mathematics, Dynamical Systems (math.DS), Dynamical Systems, Probability |
| Popis: | 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. |
| Druh dokumentu: | Article |
| ISSN: | 1553-5231 1078-0947 |
| DOI: | 10.3934/dcds.2025106 |
| DOI: | 10.48550/arxiv.2403.13416 |
| Přístupová URL adresa: | http://arxiv.org/abs/2403.13416 |
| Rights: | arXiv Non-Exclusive Distribution |
| Přístupové číslo: | edsair.doi.dedup.....8457b96aaf669bc58d212dd43f325dbd |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | 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. |
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| ISSN: | 15535231 10780947 |
| DOI: | 10.3934/dcds.2025106 |