We study infinite iterated function systems (IIFSs) consisting of bi-Lipschitz mappings instead of conformal contractions, focussing on IFSs that do not satisfy the open set condition. By assuming the logarithmic distortion property and some cardinality growth condition, we obtain a formula for the Hausdorff, box, and packing dimensions of the limit set in terms of certain topological pressure. By assuming, in addition, the weak separation condition, we show that these dimensions are equal to the growth dimension of the limit set.

中文翻译：

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由双李普希茨映射组成的无限迭代函数系统中的维数

我们研究了由双李普希茨映射而不是共形收缩组成的无限迭代函数系统 (IIFS)，重点是不满足开集条件的 IFS。通过假设对数畸变特性和一些基数增长条件，我们得到了在一定拓扑压力下设置的极限的豪斯多夫、盒子和包装尺寸的公式。此外，通过假设弱分离条件，我们表明这些维度等于极限集的增长维度。