多重循环和超循环

Pub Date : 2021-04-30 DOI:10.7146/math.scand.a-133256

Rodrigo Cardeccia, Santiago Muro

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引用次数: 8

摘要

作为$\mathcal F$-超循环的一种特殊情况，我们研究了乘法循环和超循环算子，其中$\mathcal F$是包含任意长等差数列的自然数的子集族。证明了超循环乘循环算子的几个性质，刻画了那些弱混合和弱循环的算子，并证明了有一些算子是多循环和超循环但不是弱混合的。

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Multiple recurrence and hypercyclicity

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.

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