动力系统的丰富泛函极限定理
Enriched functional limit theorems for dynamical systems
AI总结：
本文针对动力系统中大值聚类在标准Skorohod拓扑下信息丢失的问题，引入推广Whitt空间的新函数空间，并借助变换锚定尾过程导出的带装饰点过程极限定理，建立了适用于双曲与非一致扩张系统的丰富泛函极限定理。
摘要：
我们证明了在存在大值簇的情况下动力系统的泛函极限定理，这些大值在求和并适当标准化后，会在同一时间点观察到的极限过程的一个跳跃中被压缩。为了追踪在通常的 càdlàg 函数空间 Skorohod 拓扑中会丢失的聚类信息，我们引入了一个新空间，它推广了 Whitt 引入的已经更为一般的空间。我们的主要应用对象是具有重尾可观测函数的双曲和非一致扩张动力系统，这些可观测函数在动态关联的极大集（如周期点）上取得最大值。我们还研究了极值过程的极限以及不一定重尾的可观测函数的记录时点过程。所研究的应用包括双曲系统，如 Anosov 微分同胚，也包括非一致扩张映射，如具有 Benedicks-Carleson 型临界点的映射或具有 Pomeau-Manneville 或 Liverani-Saussol-Vaienti 映射中无差别不动点的映射。主要工具是一个带装饰的点过程极限定理，该定理源自一个称为变换锚定尾过程的双无限序列。
英文摘要：
We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track of the clustering information, which gets lost in the usual Skorohod topologies in the space of càdlàg functions, we introduce a new space which generalises the already more general spaces introduced by Whitt. Our main applications are to hyperbolic and non-uniformly expanding dynamical systems with heavy-tailed observable functions maximised at dynamically linked maximal sets (such as periodic points). We also study limits of extremal processes and record times point processes for observables not necessarily heavy tailed. The applications studied include hyperbolic systems such as Anosov diffeomorphisms, but also non-uniformly expanding maps such as maps with critical points of Benedicks-Carleson type or indifferent fixed points such as Pomeau-Manneville or Liverani-Saussol-Vaienti maps. The main tool is a limit theorem for point processes with decorations derived from a bi-infinite sequence called the transformed anchored tail process.
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。
