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Preprints, Working Papers, ... Year : 2024

Confined Poisson extensions

Abstract

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 $\sigma$-finite measure-preserving dynamical system $(X, \mu, T)$ and a compact extension $(X \times G, \mu \otimes m_G, T_\phi)$, then we consider the corresponding Poisson extension $((X \times G)^*, (\mu \otimes m_G)^*, (T_\phi)_*) \overset{}{\to} (X^*, \mu^*, T_*)$. 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 $(X, \mu, T)$ and a cocycle $\phi$ so that the compact extension $(X \times G, \mu \otimes m_G, T_\phi)$ has an infinite ergodic index.
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Dates and versions

hal-04511868 , version 1 (19-03-2024)

Identifiers

  • HAL Id : hal-04511868 , version 1

Cite

Séverin Benzoni, Emmanuel Roy, Thierry de la Rue. Confined Poisson extensions. 2024. ⟨hal-04511868⟩
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