Multiple recurrence and hypercyclicity

IF 0.3 4区数学 Q4 MATHEMATICS

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

Rodrigo Cardeccia, Santiago Muro

引用次数: 8

Abstract

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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多重循环和超循环

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Scandinavica 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length. Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months. All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.