论文标题
千古动作的通用扩展
Generic extensions of ergodic actions
论文作者
论文摘要
本文考虑了衡量措施保护动作的通用扩展。我们证明，具有有限的p-进入的通用扩展的p渗透性是无限的。这是通过Austin，Glasner，Thouvenot和Weiss来获得结果的，认为确定性作用的一般扩展不是同构的。我们还表明，通用的共同体是经常出现的。以及典型的延伸，可以保留光谱的奇异性，部分刚性，轻度混合和混合。同时，在通用扩展下提起某些代数特性可能取决于基础的统计特性。也考虑了典型的可测量的自动形态家庭。此类家庭的动态行为有点不寻常。它的特征是动态符合主义与通用家族代表的动态个人主义的结合。
The article considers generic extensions of measure-preserving actions. We prove that the P-entropy of the generic extensions with finite P-entropy is infinite. This is exploited to obtain the result by Austin, Glasner, Thouvenot, and Weiss that the generic extension of an deterministic action is not isomorphic to it. We show also that generic cocycles are recurrent; as well as typical extensions preserve the singularity of the spectrum, partial rigidity, mildly mixing, and mixing. At the same time, the lifting of some algebraic properties under the generic extension may depend on the statistical properties of the base. The typical measurable families of automorphisms are considered as well. The dynamic behavior of such families is a bit unusual. It is characterized by a combination of the dynamic conformism with the dynamic individualism of the representatives of the generic family.
