正则序列的鬼分布是自仿射集的仿射变换
Ghost distributions of regular sequences are affine transformations of self-affine sets
摘要：
正则序列的鬼测度是标准分形质量分布的推广。它们被用来确定类似于自动序列的正则序列的分形（或自相似）性质。Coons，Evans和Mañibo最近给出了一类正则序列的鬼测度的存在性和连续性.本文通过证明上述正则序列的鬼分布图--鬼测度的分布函数--是自仿射集的截面，给出了分形与正则序列之间的一个明确的联系。作为结果的一个应用，我们证明了Zaremba序列-差逼近数收敛的分解子的正则序列-的鬼分布都是奇异连续的.
英文摘要：
Ghost measures of regular sequences---the unbounded analogue of automatic sequences---are generalisations of standard fractal mass distributions. They were introduced to determine fractal (or self-similar) properties of regular sequences similar to those related to automatic sequences. The existence and continuity of ghost measures for a large class of regular sequences was recently given by Coons, Evans and Mañibo. In this paper, we provide an explicit connection between fractals and regular sequences by showing that the graphs of ghost distributions---the distribution functions of ghost measures---of the above-mentioned class of regular sequences are sections of self-affine sets. As an application of our result, we show that the ghost distributions of the Zaremba sequences---regular sequences of the denominators of the convergents of badly approximable numbers---are all singular continuous.
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