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arXiv · 2605.06573

Common frequently hypercyclic random vectors

Augustin Mouze·Vincent Munnier
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Abstract

We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a non-existence result. These insights are then applied to the specific setting of countable families of polynomials of weighted backward shifts, providing conditions under which they share a common frequently hypercyclic vector.

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Augustin Mouze, Vincent Munnier. 2026-05-07. Common frequently hypercyclic random vectors. https://arxiv.org/abs/2605.06573

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