标题： 自相似测度和具有共同固定点结构的集的Hausdorff维数 显示英文标题

标题： Hausdorff dimension of self-similar measures and sets with common fixed point structure

摘要： 在本文中，我们研究实线上自相似测度和集的Hausdorff维数，其中生成的迭代函数系统包含一些共享相同固定点的映射。 特别是，我们将证明，在自然参数的一个Hausdorff余维一的例外集合之外，这些系统满足弱指数分离条件。 这显著加强了第一作者与Szvák之前的结论。 作为应用，我们给出了支撑在广义4角集上的自仿射测度的Hausdorff维数。 显示英文摘要

摘要： In this paper, we study the Hausdorff dimension of self-similar measures and sets on the real line, where the generating iterated function system consists of some maps that share the same fixed point. In particular, we will show that out of a Hausdorff co-dimension one exceptional set of natural parameters, such systems satisfy a weak exponential separation. This significantly strengthens the previous result of the first author and Szv\'ak. As an application, we give the Hausdorff dimension of self-affine measures supported on the generalised 4-corner set.