多次复发和高周期性
Multiple recurrence and hypercyclicity
摘要：
本文研究了多重递归算子和超循环算子作为$\mathcal F$ -超循环算子的一种特殊情况，其中$\mathcal F$是包含任意长等差数列的自然数子集族.证明了超循环多重递归算子的几个性质，刻画了弱混合多重递归算子的特征，证明了存在多重递归超循环算子但不是弱混合算子.
英文摘要：
We study multiply recurrent and hypercyclic operators as a special case of $\mathcal F$-hypercyclicity, where $\mathcal F$ is the family of subsets of the natural numbers containing arbitrarily long arithmetic progressions. We prove several properties of hypercyclic multiply recurrent operators, we characterize those operators which are weakly mixing and multiply recurrent, and we show that there are operators that are multiply recurrent and hypercyclic but not weakly mixing.
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。
