Frequency of digits for Countable Markov maps without the big image property

没有大图像属性的可数马尔可夫映射的数字频率

• 批准号: 2278542
• 金额: --
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2278542
• 关键词: Frequency; digits; Countable; Markov; maps

There has been work on Hausdorff dimension on sets based on the frequency of digits for continued fraction expansion. This has been generalised to the setting of countable Markov maps by Fan, Jordan, Liao and Rams. However this works only when the Markov map satisfies the big image property. The project will look at the case when this property is not satisfied and make use of work by Iommi, Todd and Velozo. With his work it should be possible to give a reasonably complete answer to this problem in that setting.

对于连分式展开，已有基于位数频率的集上的豪斯多夫维数的研究。这已经被Fan， Jordan， Liao和Rams推广到可计数马尔可夫映射的设置。然而，这只在马尔可夫映射满足大图像属性时才有效。该项目将着眼于不满足该属性的情况，并利用Iommi、Todd和Velozo的工作。有了他的工作，应该有可能在那种情况下对这个问题给出一个合理完整的答案。