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： 本文解决了非一致双曲动力系统有限时间动力学和有限时间预测理论中的一些基本问题。 我们关注此类系统的相空间中的输运，并分析哪些子集以及何时轨道更倾向于访问。 获得了多项式逃逸率衰减的渐近展开式。 我们的方法基于对开放动力系统构造算子更新方程及其谱分析。 为此，我们推广了Keller-Liverani摄动技术。 考虑了大量一维非一致扩张系统的应用。 显示英文摘要

摘要： The paper addresses some basic questions in the theory of finite time dynamics and finite time predictions for non-uniformly hyperbolic dynamical systems. We are concerned with transport in phase spaces of such systems, and analyze which subsets and when the orbits prefer to visit. An asymptotic expansion of the decay of polynomial escape rates is obtained. Our approach is based on the construction of 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.