通过几乎完全增长的一般作用不存在普适零熵系统
Non-existence of a universal zero entropy system via generic actions of almost complete growth
摘要：
我们证明了可数顺从群$G$的一般p. m. p.作用具有标度熵，并且标度熵不能被给定的增长率所支配.作为推论，我们得到了不存在$G$的拓扑作用，使得其遍历不变测度集与所有遍历p. m. p. $G$ -系统的熵为零的集重合.我们还证明了剩余有限顺从群的一般作用具有标度熵，该标度熵不能由给定序列从下而上有界。我们还展示了一个顺从群的例子，它对每个自由p. m. p.作用都有这样的下界。
英文摘要：
We prove that a generic p.m.p. action of a countable amenable group $G$ has scaling entropy that can not be dominated by a given rate of growth. As a corollary, we obtain that there does not exist a topological action of $G$ for which the set of ergodic invariant measures coincides with the set of all ergodic p.m.p. $G$-systems of entropy zero. We also prove that a generic action of a residually finite amenable group has scaling entropy that can not be bounded from below by a given sequence. We also show an example of an amenable group that has such lower bound for every free p.m.p. action.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
