Belinskaya’s theorem is optimal - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Belinskaya’s theorem is optimal

Résumé

Belinskaya's theorem states that given an ergodic measure-preserving transformation, any other transformation with the same orbits and an $\mathrm{L}^1$ cocycle must be flip-conjugate to it. Our main result shows that this theorem is optimal: for all $p<1$ the integrability condition on the cocycle cannot be relaxed to being in $\mathrm{L}^p$. This also allows us to answer a question of Kerr and Li: for ergodic measure-preserving transformations, Shannon orbit equivalence doesn't boil down to flip-conjugacy.
Fichier principal
Vignette du fichier
2201.06662.pdf (429.73 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04315624 , version 1 (30-11-2023)

Identifiants

Citer

Alessandro Carderi, Matthieu Joseph, François Le Maître, Romain Tessera. Belinskaya’s theorem is optimal. 2023. ⟨hal-04315624⟩
6 Consultations
7 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More