标题： 哪些子集以及非一致双曲系统在何时倾向于访问：算子再生理论方法 显示英文标题

标题： Which subsets and when orbits of non-uniformly hyperbolic systems prefer to visit: operator renewal theory approach

摘要： 本文首次针对缓慢混合的非一致双曲动力系统在有限时间动力学和有限时间预测理论中的一些基本问题进行了探讨。 它关注此类系统的相空间中的输运问题，并分析了哪些子集以及何时轨道更倾向于访问。 得到了多项式逃逸率衰减的渐近展开式，这也允许找到首次到达概率的渐近性。 我们的方法基于对开放动力系统的新算子再生方程的构造及其谱分析。 为了做到这一点，我们推广了Keller-Liverani扰动技术。 考虑了对一大类一维非一致扩张系统应用。 显示英文摘要

摘要： The paper addresses for the first time some basic questions in the theory of finite time dynamics and finite time predictions for slowly mixing non-uniformly hyperbolic dynamical systems. It is concerned with transport in phase spaces of such systems, and analyzes which subsets and when the orbits prefer to visit. An asymptotic expansion of the decay of polynomial escape rates is obtained, which also allows for finding asymptotics of the first hitting probabilities. Our approach is based on the construction of new operator renewal equations for open dynamical systems and on their spectral analysis. In order to do this, we generalize the Keller-Liverani perturbation technique. Applications to a large class of one-dimensional non-uniformly expanding systems are considered.