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arXiv · 2402.05038

On several dynamical properties of shifts acting on directed trees

Evgeny Abakumov·Arafat Abbar
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Abstract

This paper explores the notions of $\mathcal{F}$-transitivity and topological $\mathcal{F}$-recurrence for backward shift operators on weighted $\ell^p$-spaces and $c_0$-spaces on directed trees, where $\mathcal{F}$ represents a Furstenberg family of subsets of $\mathbb{N}_0$. In particular, we establish the equivalence between recurrence and hypercyclicity of these operators on unrooted directed trees. For rooted directed trees, a backward shift operator is hypercyclic if and only if it possesses an orbit of a bounded subset that is weakly dense.

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BibTeXRIS

Evgeny Abakumov, Arafat Abbar. 2024-02-07. On several dynamical properties of shifts acting on directed trees. https://doi.org/10.4153/s0008414x24000981

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