论文标题
Belinskaya的定理是最佳的
Belinskaya's theorem is optimal
论文作者
论文摘要
Belinskaya的定理指出，鉴于具有相同轨道的任何其他转换，以及$ \ mathrm {l}^1 $ Cocycle都必须对其进行反合。我们的主要结果表明，该定理是最佳的：对于所有$ p <1 $，在$ \ mathrm {l}^p $中都不能放松Cocycle上的集成性条件。这也使我们能够回答Kerr和Li的问题：为了进行甲基殖民措施的转换，香农轨道等效性并不能归结为flip-of-of-of-chogigacy。
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.
