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

已有工作对Hausdorff维数的基础上的频率的数字集的连分数扩展。这已被推广到设置可数马尔可夫地图范，约旦，廖和公羊。然而，这仅在马尔可夫映射满足大图像性质时才有效。该项目将着眼于这种情况下，当这个属性不满意，并利用工作的Iommi，托德和Velozo。通过他的工作，应该可以在这种情况下对这个问题给出一个相当完整的答案。

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.