Abstract Recently, Liao and Rams [10] considered certain infinite iterated function systems that are natural generalizations of Gauss map. They studied the increasing rate of Birkhoff sums in such systems with polynomial decay of the derivative and calculated the Hausdorff dimensions of the sets of points whose Birkhoff sums share the same increasing rate for different unbounded potential functions. In this remark, we investigate the critical cases for the growth rate function which are not discussed in [10] .

中文翻译：

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d-衰变高斯类迭代函数系统中大Birkhoff和的注解

摘要 最近，Liao 和 Rams [10] 考虑了某些无限迭代函数系统，它们是高斯​​图的自然推广。他们研究了此类具有导数多项式衰减的系统中 Birkhoff 和的增长率，并计算了对于不同的无界势函数，Birkhoff 和具有相同增长率的点集的 Hausdorff 维数。在此评论中，我们研究了 [10] 中未讨论的增长率函数的临界情况。