Belinskaya’s theorem is optimal

Pub Date : 2022-01-17 DOI:10.4064/fm266-4-2023
A. Carderi, Matthieu Joseph, F. L. Maitre, R. Tessera
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引用次数: 1

Abstract

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.
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Belinskaya定理是最优的
Belinskaya定理指出,给定一个遍历测度保持变换,任何其他具有相同轨道和$\mathrm{L}^1$共循环的变换都必须与其翻转共轭。我们的主要结果表明,该定理是最优的:对于所有$p<1$,共循环上的可积条件不能放松为在$\mathrm{L}^ p$中。这也让我们能够回答Kerr和Li的一个问题:对于遍历测度保持变换,Shannon轨道等价不归结为翻转共轭。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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