Mixing on a class of rank-one transformations
Mixing on a class of rank-one transformations
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混合一类一级变换
DOI：
10.1017/s0143385703000464
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发表时间：
2001
影响因子：
0.9
通讯作者：
Cesar E. Silva
中科院分区：
文献类型：
--
作者：
D. Creutz;Cesar E. Silva
我们证明了一个秩一变换满足一个条件称为限制增长是一个混合变换当且仅当变换的间隔序列是一致遍历的。一致遍历性是序列遍历性概念的推广，在这个意义上，平均遍历定理适用于我们称之为动态序列的一族。本文定理的应用表明，一类多项式秩一变换，即间隔子被选择为多项式的值并对多项式有一些温和条件的秩一变换，具有限制增长性，是混合变换，这特别意味着亚当斯关于阶梯变换的结果.另一个应用程序产生了一个新的证明，奥恩斯坦的类秩一变换构造使用'随机间隔'几乎肯定是混合变换。
We prove that a rank-one transformation satisfying a condition called restricted growth is a mixing transformation if and only if the spacer sequence for the transformation is uniformly ergodic. Uniform ergodicity is a generalization of the notion of ergodicity for sequences, in the sense that the mean ergodic theorem holds for a family of what we call dynamical sequences. The application of our theorem shows that the class of polynomial rank-one transformations, rank-one transformations where the spacers are chosen to be the values of a polynomial with some mild conditions on the polynomials, that have restricted growth are mixing transformations, implying, in particular, Adams' result on staircase transformations. Another application yields a new proof that Ornstein's class of rank-one transformations constructed using ‘random spacers’ are almost surely mixing transformations.