具有可数极值集的动力系统的极值律
Extreme Value Laws for dynamical systems with countable extremal sets
摘要：
我们考虑平稳随机过程所产生的动力系统通过评估一个给定的观察沿轨道的系统。我们专注于极值行为的过程中，这是相关的入口在某些区域的相空间，这对应于邻域的最大集$\mathcal M$，即一组点的观察是最大化。这里的主要新颖之处是，我们认为，集$\mathcal M$可能有一个可数的点，这是相关的属于某个点的轨道，并可能有积累点。为了证明分布极限的存在性和研究聚类的强度，给出了极值指数，我们概括了先前在\cite{FFT12,FFT15}中引入的条件。
英文摘要：
We consider stationary stochastic processes arising from dynamical systems by evaluating a given observable along the orbits of the system. We focus on the extremal behaviour of the process, which is related to the entrance in certain regions of the phase space, which correspond to neighbourhoods of the maximal set $\mathcal M$, i.e. the set of points where the observable is maximised. The main novelty here is the fact that we consider that the set $\mathcal M$ may have a countable number of points, which are associated by belonging to the orbit of a certain point, and may have accumulation points. In order to prove the existence of distributional limits and study the intensity of clustering, given by the Extremal Index, we generalise the conditions previously introduced in \cite{FFT12,FFT15}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
