Belinskaya’s theorem is optimal

2023/01/01 by Alessandro Carderi, Matthieu Joseph, François Le Maître +1 · 4 citations
Mathematics · #Mathematics and Applications #History and Theory of Mathematics #Functional Equations Stability Results

paper · pdf · doi:10.4064/fm266-4-2023

Abstract

Belinskaya’s theorem states that given an ergodic measure-preserving transformation, any other transformation with the same orbits and an L¹ cocycle must be flip-conjugate to it. Our main result shows that this theorem is optimal: for all p \lt 1 the

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• The analogue of Belinskaya's theorem for measure-preserving flows
• Weakly mixing transformation that is Shannon orbit equivalent to a given ergodic transformation
• Entropy, virtual Abelianness and Shannon orbit equivalence
• Quantitative orbit equivalence for ℤ-odometers

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