论文标题
线性动力学中的算术进程和混乱
Arithmetic progressions and chaos in linear dynamics
论文作者
论文摘要
我们根据返回时间集中的长期算术进程的存在，在反射性Banach空间上表征混乱的线性算子。为了实现这一目标，我们研究了$ \ Mathcal F $ - 流行循环，用于与任意长期算术进程相关的自然数量的家庭。我们研究了它们与线性动力学中不同概念的联系。
We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. To achieve this, we study $\mathcal F$-hypercyclicity for a family of subsets of the natural numbers associated with the existence of arbitrarily long arithmetic progressions. We investigate their connection with different concepts in linear dynamics.
