论文标题
在动态系统中覆盖时间
Cover times in dynamical systems
论文作者
论文摘要
考虑到一维动力学系统，我们研究其覆盖时间，该系统量化了轨道在状态空间中变得稠密的速率。使用转移操作员工具用于具有孔和诱导技术的动力系统，对于一系列统一的双曲线和非统一双曲线系统，我们就最低度量球的衰减率表示了预期覆盖时间的渐近公式。应用包括高斯地图和Manneville-Pomeau地图。
Given a one-dimensional dynamical system we study its cover time, which quantifies the rate at which orbits become dense in the state space. Using transfer operator tools for dynamical systems with holes and inducing techniques, for a wide class of uniformly hyperbolic and non-uniformly hyperbolic systems we obtain an asymptotic formula for the expected cover time in terms of the decay rate of the measure of the ball of minimum measure. Applications include the Gauss map and Manneville-Pomeau maps.
