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 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 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.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)