In this paper, we look at a family of Renyi-like continued fraction expansions and the associated conformal iterated function systems. We show that for every $k\ge 2$, every such associated system has full Hausdorff dimension spectrum. We construct two examples of iterated function systems that do not have full Hausdorff dimension spectrum. One is a subsystem of any given Renyi-like system, while the second consists of similarities.

中文翻译：

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类人参连续馏分的Hausdorff维数谱

在本文中，我们着眼于一类类似于Renyi的连续分数展开式和相关的共形迭代函数系统。我们证明了每一个$ķ\ge \mathrm{2个}$，每个这样的关联系统都具有完整的Hausdorff维数谱。我们构造了两个没有完整Hausdorff维数谱的迭代函数系统的示例。第一个是任何给定的类似于Renyi的系统的子系统，而第二个则由相似性组成。