Multiple recurrence and hypercyclicity

Rodrigo Cardeccia; Santiago Muro

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arXiv · 2104.15033

Multiple recurrence and hypercyclicity

Rodrigo Cardeccia·Santiago Muro

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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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Rodrigo Cardeccia, Santiago Muro. 2021-04-30. Multiple recurrence and hypercyclicity. https://arxiv.org/abs/2104.15033

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