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Pré-Publication, Document De Travail Année : 2022

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.
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Dates et versions

hal-03989599 , version 1 (14-02-2023)

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Alessandro Carderi, Matthieu Joseph, François Le Maître, Romain Tessera. Belinskaya's theorem is optimal. 2023. ⟨hal-03989599⟩
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