We study the existence of limiting laws of rare events corresponding to the entrance of the orbits on certain target sets in the phase space. The limiting laws are obtained when the target sets shrink to a Cantor set of zero Lebesgue measure. We consider both the presence and absence of clustering, which is detected by the Extremal Index, which turns out to be very useful to identify the compatibility between the dynamics and the fractal structure of the limiting Cantor set. The computation of the Extremal Index is connected to the box dimension of the intersection between the Cantor set and its iterates.

中文翻译：

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康托目标集的罕见事件

我们研究了与相空间中某些目标集上的轨道入口相对应的罕见事件的极限定律的存在性。当目标集收缩到零勒贝格测度的康托集时，就得到了极限律。我们考虑了聚类的存在和不存在，这是由极值指数检测到的，结果证明这对于识别限制康托集的动力学和分形结构之间的兼容性非常有用。极值指数的计算与康托集及其迭代之间的交集的框维度有关。